spacegroupdata.py

# Copyright 2010 Torbjorn Bjorkman
# This file is part of cif2cell
#
# cif2cell is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# cif2cell is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with cif2cell.  If not, see <http://www.gnu.org/licenses/>.
#
#******************************************************************************************
#  Description: Contains:
#               HM2Hall       : Dictionary for going from Hermann-Mauguin symbol to Hall symbol.
#                               If support is lacking for some HM setting, then add to this dict.
#               Hall2HM       : Dictionary for going from Hall symbol to Hermann-Mauguin symbol.
#               Hall2Number   : Dictionary for going from Hall symbol to space group number (integer).
#               Number2Hall   : Dictionary for going from number to Hall symbol. Only contains
#                               space groups with unique settings.
#               Rhomb2HexHall : Dictionary with hexagonal setting of a space group corresponding
#                               to some rhombohedral setting.
#               Hex2RhombHall : The reverse of Rhomb2HexHall.
#               SymOpsHall    : Dictionary of the set of equivalent positions in XYZ-format.
#                               Example :
#                                     SymOpsHall['C 2y'] = [['x','y','z'],
#                                                           ['-x','y','-z'],
#                                                           ['x+1/2','y+1/2','z'],
#                                                           ['-x+1/2','y+1/2','-z']]
#
#               All data was generated using the sginfo program (http://cci.lbl.gov/sginfo)
#               and automatically processed into python code.
#
#  Author:      Torbjorn Bjorkman, torbjorn.bjorkman(at)aalto.fi
#  Affiliation: COMP, Aaalto University School of Science,
#               Department of Applied Physics, Espoo, Finland
#
#******************************************************************************************

# Convert Hermann-Mauguin symbol to Hall symbol
# Just keep adding new HM string representations until we support everything.
# The ICSD convention of denoting setting shifted from the origin with S and
# the non-shifted with Z is fully supported.
HM2Hall = {
    #   1
    'P1' : 'P 1',
    #   2
    'P-1' : '-P 1',
    #   3
    'P2' : 'P 2y',
    'P2:b' : 'P 2y',
    'P2b' : 'P 2y',
    'P121' : 'P 2y',
    'P2:c' : 'P 2',
    'P2c' : 'P 2',
    'P112' : 'P 2',
    'P2:a' : 'P 2x',
    'P2a' : 'P 2x',
    'P211' : 'P 2x',
    #   4
    'P21' : 'P 2yb',
    'P21:b' : 'P 2yb',
    'P21b' : 'P 2yb',
    'P1211' : 'P 2yb',
    'P21:c' : 'P 2c',
    'P21c' : 'P 2c',
    'P1121' : 'P 2c',
    'P21:a' : 'P 2xa',
    'P21a' : 'P 2xa',
    'P2111' : 'P 2xa',
    #   5
    'C2' : 'C 2y',
    'C2:b1' : 'C 2y',
    'C2b1' : 'C 2y',
    'C121' : 'C 2y',
    'C2:b2' : 'A 2y',
    'C2b2' : 'A 2y',
    'A121' : 'A 2y',
    'A2' : 'A 2y',
    'C2:b3' : 'I 2y',
    'C2b3' : 'I 2y',
    'I121' : 'I 2y',
    'I2' : 'I 2y',
    'C2:c1' : 'A 2',
    'C2c1' : 'A 2',
    'A112' : 'A 2',
    'C2:c2' : 'B 2',
    'C2c2' : 'B 2',
    'B112' : 'B 2',
    'B2' : 'B 2',
    'C2:c3' : 'I 2',
    'C2c3' : 'I 2',
    'I112' : 'I 2',
    'C2:a1' : 'B 2x',
    'C2a1' : 'B 2x',
    'B211' : 'B 2x',
    'C2:a2' : 'C 2x',
    'C2a2' : 'C 2x',
    'C211' : 'C 2x',
    'C2:a3' : 'I 2x',
    'C2a3' : 'I 2x',
    'I211' : 'I 2x',
    #   6
    'Pm' : 'P -2y',
    'Pm:b' : 'P -2y',
    'Pmb' : 'P -2y',
    'P1m1' : 'P -2y',
    'Pm:c' : 'P -2',
    'Pmc' : 'P -2',
    'P11m' : 'P -2',
    'Pm:a' : 'P -2x',
    'Pma' : 'P -2x',
    'Pm11' : 'P -2x',
    #   7
    'Pc' : 'P -2yc',
    'Pc:b1' : 'P -2yc',
    'Pcb1' : 'P -2yc',
    'P1c1' : 'P -2yc',
    'Pc:b2' : 'P -2yac',
    'Pcb2' : 'P -2yac',
    'P1n1' : 'P -2yac',
    'Pn' : 'P -2yac',
    'Pc:b3' : 'P -2ya',
    'Pcb3' : 'P -2ya',
    'P1a1' : 'P -2ya',
    'Pa' : 'P -2ya',
    'Pc:c1' : 'P -2a',
    'Pcc1' : 'P -2a',
    'P11a' : 'P -2a',
    'Pc:c2' : 'P -2ab',
    'Pcc2' : 'P -2ab',
    'P11n' : 'P -2ab',
    'Pc:c3' : 'P -2b',
    'Pcc3' : 'P -2b',
    'P11b' : 'P -2b',
    'Pb' : 'P -2b',
    'Pc:a1' : 'P -2xb',
    'Pca1' : 'P -2xb',
    'Pb11' : 'P -2xb',
    'Pc:a2' : 'P -2xbc',
    'Pca2' : 'P -2xbc',
    'Pn11' : 'P -2xbc',
    'Pc:a3' : 'P -2xc',
    'Pca3' : 'P -2xc',
    'Pc11' : 'P -2xc',
    'B1a1' : 'B -2yc',
    #   8
    'Cm' : 'C -2y',
    'Cm:b1' : 'C -2y',
    'Cmb1' : 'C -2y',
    'C1m1' : 'C -2y',
    'Cm:b2' : 'A -2y',
    'Cmb2' : 'A -2y',
    'A1m1' : 'A -2y',
    'Cm:b3' : 'I -2y',
    'Cmb3' : 'I -2y',
    'I1m1' : 'I -2y',
    'Im' : 'I -2y',
    'Cm:c1' : 'A -2',
    'Cmc1' : 'A -2',
    'A11m' : 'A -2',
    'Cm:c2' : 'B -2',
    'Cmc2' : 'B -2',
    'B11m' : 'B -2',
    'Bm' : 'B -2',
    'Cm:c3' : 'I -2',
    'Cmc3' : 'I -2',
    'I11m' : 'I -2',
    'Cm:a1' : 'B -2x',
    'Cma1' : 'B -2x',
    'Bm11' : 'B -2x',
    'Cm:a2' : 'C -2x',
    'Cma2' : 'C -2x',
    'Cm11' : 'C -2x',
    'Cm:a3' : 'I -2x',
    'Cma3' : 'I -2x',
    'Im11' : 'I -2x',
    #   9
    'Cc' : 'C -2yc',
    'Cc:b1' : 'C -2yc',
    'Ccb1' : 'C -2yc',
    'C1c1' : 'C -2yc',
    'Cc:b2' : 'A -2yac',
    'Ccb2' : 'A -2yac',
    'A1n1' : 'A -2yac',
    'Cc:b3' : 'I -2ya',
    'Ccb3' : 'I -2ya',
    'I1a1' : 'I -2ya',
    'Ia' : 'I -2ya',
    'Cc:-b1' : 'A -2ya',
    'Cc-b1' : 'A -2ya',
    'A1a1' : 'A -2ya',
    'Aa' : 'A -2ya',
    'Cc:-b2' : 'C -2ybc',
    'Cc-b2' : 'C -2ybc',
    'C1n1' : 'C -2ybc',
    'Cc:-b3' : 'I -2yc',
    'Cc-b3' : 'I -2yc',
    'I1c1' : 'I -2yc',
    'Cc:c1' : 'A -2a',
    'Ccc1' : 'A -2a',
    'A11a' : 'A -2a',
    'Cc:c2' : 'B -2bc',
    'B11n' : 'B -2bc',
    'Cc:c3' : 'I -2b',
    'Ccc3' : 'I -2b',
    'I11b' : 'I -2b',
    'Ib' : 'I -2b',
    'Cc:-c1' : 'B -2b',
    'Cc-c1' : 'B -2b',
    'B11b' : 'B -2b',
    'Bb' : 'B -2b',
    'Cc:-c2' : 'A -2ac',
    'Cc-c2' : 'A -2ac',
    'A11n' : 'A -2ac',
    'Cc:-c3' : 'I -2a',
    'Cc-c3' : 'I -2a',
    'I11a' : 'I -2a',
    'Cc:a1' : 'B -2xb',
    'Cca1' : 'B -2xb',
    'Bb11' : 'B -2xb',
    'Cc:a2' : 'C -2xbc',
    'Cca2' : 'C -2xbc',
    'Cn11' : 'C -2xbc',
    'Cc:a3' : 'I -2xc',
    'Cca3' : 'I -2xc',
    'Ic11' : 'I -2xc',
    'Cc:-a1' : 'C -2xc',
    'Cc-a1' : 'C -2xc',
    'Cc11' : 'C -2xc',
    'Cc:-a2' : 'B -2xbc',
    'Cc-a2' : 'B -2xbc',
    'Bn11' : 'B -2xbc',
    'Cc:-a3' : 'I -2xb',
    'Cc-a3' : 'I -2xb',
    'Ib11' : 'I -2xb',
    #  10
    'P2/m' : '-P 2y',
    'P2/m:b' : '-P 2y',
    'P2/mb' : '-P 2y',
    'P12/m1' : '-P 2y',
    'P2/m:c' : '-P 2',
    'P2/mc' : '-P 2',
    'P112/m' : '-P 2',
    'P2/m:a' : '-P 2x',
    'P2/ma' : '-P 2x',
    'P2/m11' : '-P 2x',
    #  11
    'P21/m' : '-P 2yb',
    'P21/m:b' : '-P 2yb',
    'P21/mb' : '-P 2yb',
    'P121/m1' : '-P 2yb',
    'P21/m:c' : '-P 2c',
    'P21/mc' : '-P 2c',
    'P1121/m' : '-P 2c',
    'P21/m:a' : '-P 2xa',
    'P21/ma' : '-P 2xa',
    'P21/m11' : '-P 2xa',
    #  12
    'C2/m' : '-C 2y',
    'C2/m:b1' : '-C 2y',
    'C2/mb1' : '-C 2y',
    'C12/m1' : '-C 2y',
    'C2/m:b2' : '-A 2y',
    'C2/mb2' : '-A 2y',
    'A12/m1' : '-A 2y',
    'A2/m' : '-A 2y',
    'C2/m:b3' : '-I 2y',
    'C2/mb3' : '-I 2y',
    'I12/m1' : '-I 2y',
    'I2/m' : '-I 2y',
    'C2/m:c1' : '-A 2',
    'C2/mc1' : '-A 2',
    'A112/m' : '-A 2',
    'C2/m:c2' : '-B 2',
    'C2/mc2' : '-B 2',
    'B112/m' : '-B 2',
    'B2/m' : '-B 2',
    'C2/m:c3' : '-I 2',
    'C2/mc3' : '-I 2',
    'I112/m' : '-I 2',
    'C2/m:a1' : '-B 2x',
    'C2/ma1' : '-B 2x',
    'B2/m11' : '-B 2x',
    'C2/m:a2' : '-C 2x',
    'C2/ma2' : '-C 2x',
    'C2/m11' : '-C 2x',
    'C2/m:a3' : '-I 2x',
    'C2/ma3' : '-I 2x',
    'I2/m11' : '-I 2x',
    #  13
    'P2/c' : '-P 2yc',
    'P2/c:b1' : '-P 2yc',
    'P2/cb1' : '-P 2yc',
    'P12/c1' : '-P 2yc',
    'P2/c:b2' : '-P 2yac',
    'P2/cb2' : '-P 2yac',
    'P12/n1' : '-P 2yac',
    'P2/n' : '-P 2yac',
    'P2/c:b3' : '-P 2ya',
    'P2/cb3' : '-P 2ya',
    'P12/a1' : '-P 2ya',
    'P2/a' : '-P 2ya',
    'P2/c:c1' : '-P 2a',
    'P2/cc1' : '-P 2a',
    'P112/a' : '-P 2a',
    'P2/c:c2' : '-P 2ab',
    'P2/cc2' : '-P 2ab',
    'P112/n' : '-P 2ab',
    'P2/c:c3' : '-P 2b',
    'P2/cc3' : '-P 2b',
    'P112/b' : '-P 2b',
    'P2/b' : '-P 2b',
    'P2/c:a1' : '-P 2xb',
    'P2/ca1' : '-P 2xb',
    'P2/b11' : '-P 2xb',
    'P2/c:a2' : '-P 2xbc',
    'P2/ca2' : '-P 2xbc',
    'P2/n11' : '-P 2xbc',
    'P2/c:a3' : '-P 2xc',
    'P2/ca3' : '-P 2xc',
    'P2/c11' : '-P 2xc',
    #  14
    'P21/c' : '-P 2ybc',
    'P21/c:b1' : '-P 2ybc',
    'P21/cb1' : '-P 2ybc',
    'P121/c1' : '-P 2ybc',
    'P21/c:b2' : '-P 2yn',
    'P21/cb2' : '-P 2yn',
    'P121/n1' : '-P 2yn',
    'P21/n' : '-P 2yn',
    'P21/c:b3' : '-P 2yab',
    'P21/cb3' : '-P 2yab',
    'P121/a1' : '-P 2yab',
    'P21/a' : '-P 2yab',
    'P21/c:c1' : '-P 2ac',
    'P21/cc1' : '-P 2ac',
    'P1121/a' : '-P 2ac',
    'P21/c:c2' : '-P 2n',
    'P21/cc2' : '-P 2n',
    'P1121/n' : '-P 2n',
    'P21/c:c3' : '-P 2bc',
    'P21/cc3' : '-P 2bc',
    'P1121/b' : '-P 2bc',
    'P21/b' : '-P 2bc',
    'P21/c:a1' : '-P 2xab',
    'P21/ca1' : '-P 2xab',
    'P21/b11' : '-P 2xab',
    'P21/c:a2' : '-P 2xn',
    'P21/ca2' : '-P 2xn',
    'P21/n11' : '-P 2xn',
    'P21/c:a3' : '-P 2xac',
    'P21/ca3' : '-P 2xac',
    'P21/c11' : '-P 2xac',
    'B121/c1' : '-B 2ybc',
    #  15
    'C2/c' : '-C 2yc',
    'C2/c:b1' : '-C 2yc',
    'C2/cb1' : '-C 2yc',
    'C12/c1' : '-C 2yc',
    'C2/c:b2' : '-A 2yac',
    'C2/cb2' : '-A 2yac',
    'A12/n1' : '-A 2yac',
    'A2/n' : '-A 2yac',
    'C2/c:b3' : '-I 2ya',
    'C2/cb3' : '-I 2ya',
    'I12/a1' : '-I 2ya',
    'I2/a' : '-I 2ya',
    'C2/c:-b1' : '-A 2ya',
    'C2/c-b1' : '-A 2ya',
    'A12/a1' : '-A 2ya',
    'A2/a' : '-A 2ya',
    'C2/c:-b2' : '-C 2ybc',
    'C2/c-b2' : '-C 2ybc',
    'C12/n1' : '-C 2ybc',
    'C2/c:-b3' : '-I 2yc',
    'C2/c-b3' : '-I 2yc',
    'I12/c1' : '-I 2yc',
    'I2/c' : '-I 2yc',
    'C2/c:c1' : '-A 2a',
    'C2/cc1' : '-A 2a',
    'A112/a' : '-A 2a',
    'C2/c:c2' : '-B 2bc',
    'C2/cc2' : '-B 2bc',
    'B112/n' : '-B 2bc',
    'B2/n' : '-B 2bc',
    'C2/c:c3' : '-I 2b',
    'C2/cc3' : '-I 2b',
    'I112/b' : '-I 2b',
    'I2/b' : '-I 2b',
    'C2/c:-c1' : '-B 2b',
    'C2/c-c1' : '-B 2b',
    'B112/b' : '-B 2b',
    'B2/b' : '-B 2b',
    'C2/c:-c2' : '-A 2ac',
    'C2/c-c2' : '-A 2ac',
    'A112/n' : '-A 2ac',
    'C2/c:-c3' : '-I 2a',
    'C2/c-c3' : '-I 2a',
    'I112/a' : '-I 2a',
    'C2/c:a1' : '-B 2xb',
    'C2/ca1' : '-B 2xb',
    'B2/b11' : '-B 2xb',
    'C2/c:a2' : '-C 2xbc',
    'C2/ca2' : '-C 2xbc',
    'C2/n11' : '-C 2xbc',
    'C2/c:a3' : '-I 2xc',
    'C2/ca3' : '-I 2xc',
    'I2/c11' : '-I 2xc',
    'C2/c:-a1' : '-C 2xc',
    'C2/c-a1' : '-C 2xc',
    'C2/c11' : '-C 2xc',
    'C2/c:-a2' : '-B 2xbc',
    'C2/c-a2' : '-B 2xbc',
    'B2/n11' : '-B 2xbc',
    'C2/c:-a3' : '-I 2xb',
    'C2/c-a3' : '-I 2xb',
    'I2/b11' : '-I 2xb',
    #  16
    'P222' : 'P 2 2',
    #  17
    'P2221' : 'P 2c 2',
    'P2122' : 'P 2a 2a',
    'P2212' : 'P 2 2b',
    #  18
    'P21212' : 'P 2 2ab',
    'P22121' : 'P 2bc 2',
    'P21221' : 'P 2ac 2ac',
    #  19
    'P212121' : 'P 2ac 2ab',
    #  20
    'C2221' : 'C 2c 2',
    'C2221S' : 'C 2c 2',
    'A2122' : 'A 2a 2a',
    'B2212' : 'B 2 2b',
    #  21
    'C222' : 'C 2 2',
    'A222' : 'A 2 2',
    'B222' : 'B 2 2',
    #  22
    'F222' : 'F 2 2',
    #  23
    'I222' : 'I 2 2',
    #  24
    'I212121' : 'I 2b 2c',
    #  25
    'Pmm2' : 'P 2 -2',
    'P2mm' : 'P -2 2',
    'Pm2m' : 'P -2 -2',
    #  26
    'Pmc21' : 'P 2c -2',
    'Pcm21' : 'P 2c -2c',
    'P21ma' : 'P -2a 2a',
    'P21am' : 'P -2 2a',
    'Pb21m' : 'P -2 -2b',
    'Pm21b' : 'P -2b -2',
    #  27
    'Pcc2' : 'P 2 -2c',
    'P2aa' : 'P -2a 2',
    'Pb2b' : 'P -2b -2b',
    #  28
    'Pma2' : 'P 2 -2a',
    'Pbm2' : 'P 2 -2b',
    'P2mb' : 'P -2b 2',
    'P2cm' : 'P -2c 2',
    'Pc2m' : 'P -2c -2c',
    'Pm2a' : 'P -2a -2a',
    #  29
    'Pca21' : 'P 2c -2ac',
    'Pbc21' : 'P 2c -2b',
    'P21ab' : 'P -2b 2a',
    'P21ca' : 'P -2ac 2a',
    'Pc21b' : 'P -2bc -2c',
    'Pb21a' : 'P -2a -2ab',
    #  30
    'Pnc2' : 'P 2 -2bc',
    'Pcn2' : 'P 2 -2ac',
    'P2na' : 'P -2ac 2',
    'P2an' : 'P -2ab 2',
    'Pb2n' : 'P -2ab -2ab',
    'Pn2b' : 'P -2bc -2bc',
    #  31
    'Pmn21' : 'P 2ac -2',
    'Pnm21' : 'P 2bc -2bc',
    'P21mn' : 'P -2ab 2ab',
    'P21nm' : 'P -2 2ac',
    'Pn21m' : 'P -2 -2bc',
    'Pm21n' : 'P -2ab -2',
    #  32
    'Pba2' : 'P 2 -2ab',
    'P2cb' : 'P -2bc 2',
    'Pc2a' : 'P -2ac -2ac',
    #  33
    'Pna21' : 'P 2c -2n',
    'Pbn21' : 'P 2c -2ab',
    'P21nb' : 'P -2bc 2a',
    'P21cn' : 'P -2n 2a',
    'Pc21n' : 'P -2n -2ac',
    'Pn21a' : 'P -2ac -2n',
    #  34
    'Pnn2' : 'P 2 -2n',
    'P2nn' : 'P -2n 2',
    'Pn2n' : 'P -2n -2n',
    #  35
    'Cmm2' : 'C 2 -2',
    'A2mm' : 'A -2 2',
    'Bm2m' : 'B -2 -2',
    #  36
    'Cmc21' : 'C 2c -2',
    'Ccm21' : 'C 2c -2c',
    'A21ma' : 'A -2a 2a',
    'A21am' : 'A -2 2a',
    'Bb21m' : 'B -2 -2b',
    'Bm21b' : 'B -2b -2',
    #  37
    'Ccc2' : 'C 2 -2c',
    'A2aa' : 'A -2a 2',
    'Bb2b' : 'B -2b -2b',
    #  38
    'Amm2' : 'A 2 -2',
    'Bmm2' : 'B 2 -2',
    'B2mm' : 'B -2 2',
    'C2mm' : 'C -2 2',
    'Cm2m' : 'C -2 -2',
    'Am2m' : 'A -2 -2',
    #  39
    'Abm2' : 'A 2 -2c',
    'Bma2' : 'B 2 -2c',
    'B2cm' : 'B -2c 2',
    'C2mb' : 'C -2b 2',
    'Cm2a' : 'C -2b -2b',
    'Ac2m' : 'A -2c -2c',
    #  40
    'Ama2' : 'A 2 -2a',
    'Bbm2' : 'B 2 -2b',
    'B2mb' : 'B -2b 2',
    'C2cm' : 'C -2c 2',
    'Cc2m' : 'C -2c -2c',
    'Am2a' : 'A -2a -2a',
    #  41
    'Aba2' : 'A 2 -2ac',
    'Bba2' : 'B 2 -2bc',
    'B2cb' : 'B -2bc 2',
    'C2cb' : 'C -2bc 2',
    'Cc2a' : 'C -2bc -2bc',
    'Ac2a' : 'A -2ac -2ac',
    #  42
    'Fmm2' : 'F 2 -2',
    'F2mm' : 'F -2 2',
    'Fm2m' : 'F -2 -2',
    #  43
    'Fdd2' : 'F 2 -2d',
    'F2dd' : 'F -2d 2',
    'Fd2d' : 'F -2d -2d',
    #  44
    'Imm2' : 'I 2 -2',
    'I2mm' : 'I -2 2',
    'Im2m' : 'I -2 -2',
    #  45
    'Iba2' : 'I 2 -2c',
    'I2cb' : 'I -2a 2',
    'Ic2a' : 'I -2b -2b',
    #  46
    'Ima2' : 'I 2 -2a',
    'Ibm2' : 'I 2 -2b',
    'I2mb' : 'I -2b 2',
    'I2cm' : 'I -2c 2',
    'Ic2m' : 'I -2c -2c',
    'Im2a' : 'I -2a -2a',
    #  47
    'Pmmm' : '-P 2 2',
    'P2/m2/m2/m' : '-P 2 2',
    #  48
    'Pnnn' : 'P 2 2 -1n',
    'Pnnn:1' : 'P 2 2 -1n',
    'Pnnn1' : 'P 2 2 -1n',
    'PnnnS' : 'P 2 2 -1n',
    'Pnnn:2' : '-P 2ab 2bc',
    'Pnnn2' : '-P 2ab 2bc',
    'PnnnZ' : '-P 2ab 2bc',
    #  49
    'Pccm' : '-P 2 2c',
    'Pmaa' : '-P 2a 2',
    'Pbmb' : '-P 2b 2b',
    #  50
    'Pban' : 'P 2 2 -1ab',
    'Pban:1' : 'P 2 2 -1ab',
    'Pban1' : 'P 2 2 -1ab',
    'PbanS' : 'P 2 2 -1ab',
    'Pban:2' : '-P 2ab 2b',
    'Pban2' : '-P 2ab 2b',
    'PbanZ' : '-P 2ab 2b',
    'Pncb' : 'P 2 2 -1bc',
    'Pncb:1' : 'P 2 2 -1bc',
    'Pncb1' : 'P 2 2 -1bc',
    'PncbS' : 'P 2 2 -1bc',
    'Pncb:2' : '-P 2b 2bc',
    'Pncb2' : '-P 2b 2bc',
    'PncbZ' : '-P 2b 2bc',
    'Pcna' : 'P 2 2 -1ac',
    'Pcna:1' : 'P 2 2 -1ac',
    'Pcna1' : 'P 2 2 -1ac',
    'PcnaS' : 'P 2 2 -1ac',
    'Pcna:2' : '-P 2a 2c',
    'Pcna2' : '-P 2a 2c',
    'PcnaZ' : '-P 2a 2c',
    #  51
    'Pmma' : '-P 2a 2a',
    'Pmmb' : '-P 2b 2',
    'Pbmm' : '-P 2 2b',
    'Pcmm' : '-P 2c 2c',
    'Pmcm' : '-P 2c 2',
    'Pmam' : '-P 2 2a',
    #  52
    'Pnna' : '-P 2a 2bc',
    'Pnnb' : '-P 2b 2n',
    'Pbnn' : '-P 2n 2b',
    'Pcnn' : '-P 2ab 2c',
    'Pncn' : '-P 2ab 2n',
    'Pnan' : '-P 2n 2bc',
    #  53
    'Pmna' : '-P 2ac 2',
    'Pnmb' : '-P 2bc 2bc',
    'Pbmn' : '-P 2ab 2ab',
    'Pcnm' : '-P 2 2ac',
    'Pncm' : '-P 2 2bc',
    'Pman' : '-P 2ab 2',
    #  54
    'Pcca' : '-P 2a 2ac',
    'Pccb' : '-P 2b 2c',
    'Pbaa' : '-P 2a 2b',
    'Pcaa' : '-P 2ac 2c',
    'Pbcb' : '-P 2bc 2b',
    'Pbab' : '-P 2b 2ab',
    #  55
    'Pbam' : '-P 2 2ab',
    'Pmcb' : '-P 2bc 2',
    'Pcma' : '-P 2ac 2ac',
    #  56
    'Pccn' : '-P 2ab 2ac',
    'Pnaa' : '-P 2ac 2bc',
    'Pbnb' : '-P 2bc 2ab',
    #  57
    'Pbcm' : '-P 2c 2b',
    'Pcam' : '-P 2c 2ac',
    'Pmca' : '-P 2ac 2a',
    'Pmab' : '-P 2b 2a',
    'Pbma' : '-P 2a 2ab',
    'Pcmb' : '-P 2bc 2c',
    #  58
    'Pnnm' : '-P 2 2n',
    'Pmnn' : '-P 2n 2',
    'Pnmn' : '-P 2n 2n',
    #  59
    'Pmmn' : 'P 2 2ab -1ab',
    'Pmmn:1' : 'P 2 2ab -1ab',
    'Pmmn1' : 'P 2 2ab -1ab',
    'PmmnS' : 'P 2 2ab -1ab',
    'Pmmn:2' : '-P 2ab 2a',
    'Pmmn2' : '-P 2ab 2a',
    'PmmnZ' : '-P 2ab 2a',
    'Pnmm' : 'P 2bc 2 -1bc',
    'Pnmm:1' : 'P 2bc 2 -1bc',
    'Pnmm1' : 'P 2bc 2 -1bc',
    'PnmmS' : 'P 2bc 2 -1bc',
    'Pnmm:2' : '-P 2c 2bc',
    'Pnmm2' : '-P 2c 2bc',
    'PnmmZ' : '-P 2c 2bc',
    'Pmnm' : 'P 2ac 2ac -1ac',
    'Pmnm:1' : 'P 2ac 2ac -1ac',
    'Pmnm1' : 'P 2ac 2ac -1ac',
    'PmnmS' : 'P 2ac 2ac -1ac',
    'Pmnm:2' : '-P 2c 2a',
    'Pmnm2' : '-P 2c 2a',
    'PmnmZ' : '-P 2c 2a',
    #  60
    'Pbcn' : '-P 2n 2ab',
    'Pcan' : '-P 2n 2c',
    'Pnca' : '-P 2a 2n',
    'Pnab' : '-P 2bc 2n',
    'Pbna' : '-P 2ac 2b',
    'Pcnb' : '-P 2b 2ac',
    #  61
    'Pbca' : '-P 2ac 2ab',
    'P21/b21/c21/a' : '-P 2ac 2ab',
    'Pcab' : '-P 2bc 2ac',
    #  62
    'Pnma' : '-P 2ac 2n',
    'Pmnb' : '-P 2bc 2a',
    'Pbnm' : '-P 2c 2ab',
    'Pcmn' : '-P 2n 2ac',
    'Pmcn' : '-P 2n 2a',
    'Pnam' : '-P 2c 2n',
    #  63
    'Cmcm' : '-C 2c 2',
    'Ccmm' : '-C 2c 2c',
    'Amma' : '-A 2a 2a',
    'Amam' : '-A 2 2a',
    'Bbmm' : '-B 2 2b',
    'Bmmb' : '-B 2b 2',
    #  64
    'Cmca' : '-C 2bc 2',
    'Cmce' : '-C 2bc 2',
    'Ccmb' : '-C 2bc 2bc',
    'Abma' : '-A 2ac 2ac',
    'Acam' : '-A 2 2ac',
    'Bbcm' : '-B 2 2bc',
    'Bmab' : '-B 2bc 2',
    #  65
    'Cmmm' : '-C 2 2',
    'Ammm' : '-A 2 2',
    'Bmmm' : '-B 2 2',
    'C2/m2/m2/m' : '-C 2 2',
    'A2/m2/m2/m' : '-A 2 2',
    'B2/m2/m2/m' : '-B 2 2',
    #  66
    'Cccm' : '-C 2 2c',
    'Amaa' : '-A 2a 2',
    'Bbmb' : '-B 2b 2b',
    #  67
    'Cmma' : '-C 2b 2',
    'Cmmb' : '-C 2b 2b',
    'Abmm' : '-A 2c 2c',
    'Acmm' : '-A 2 2c',
    'Bmcm' : '-B 2 2c',
    'Bmam' : '-B 2c 2',
    #  68
    'Ccca' : 'C 2 2 -1bc',
    'Ccca:1' : 'C 2 2 -1bc',
    'Ccca1' : 'C 2 2 -1bc',
    'CccaS' : 'C 2 2 -1bc',
    'Ccca:2' : '-C 2b 2bc',
    'Ccca2' : '-C 2b 2bc',
    'CccaZ' : '-C 2b 2bc',
    'Cccb' : 'C 2 2 -1bc',
    'Cccb:1' : 'C 2 2 -1bc',
    'Cccb1' : 'C 2 2 -1bc',
    'CccbS' : 'C 2 2 -1bc',
    'Cccb:2' : '-C 2b 2c',
    'Cccb2' : '-C 2b 2c',
    'CccbZ' : '-C 2b 2c',
    'Abaa' : 'A 2 2 -1ac',
    'Abaa:1' : 'A 2 2 -1ac',
    'Abaa1' : 'A 2 2 -1ac',
    'AbaaS' : 'A 2 2 -1ac',
    'Abaa:2' : '-A 2a 2c',
    'Abaa2' : '-A 2a 2c',
    'AbaaZ' : '-A 2a 2c',
    'Acaa' : 'A 2 2 -1ac',
    'Acaa:1' : 'A 2 2 -1ac',
    'Acaa1' : 'A 2 2 -1ac',
    'AcaaS' : 'A 2 2 -1ac',
    'Acaa:2' : '-A 2ac 2c',
    'Acaa2' : '-A 2ac 2c',
    'AcaaZ' : '-A 2ac 2c',
    'Bbcb' : 'B 2 2 -1bc',
    'Bbcb:1' : 'B 2 2 -1bc',
    'Bbcb1' : 'B 2 2 -1bc',
    'BbcbS' : 'B 2 2 -1bc',
    'Bbcb:2' : '-B 2bc 2b',
    'Bbcb2' : '-B 2bc 2b',
    'BbcbZ' : '-B 2bc 2b',
    'Bbab' : 'B 2 2 -1bc',
    'Bbab:1' : 'B 2 2 -1bc',
    'Bbab1' : 'B 2 2 -1bc',
    'BbabS' : 'B 2 2 -1bc',
    'Bbab:2' : '-B 2b 2bc',
    'Bbab2' : '-B 2b 2bc',
    'BbabZ' : '-B 2b 2bc',
    #  69
    'Fmmm' : '-F 2 2',
    'F2/m2/m2/m' : '-F 2 2',
    #  70
    'Fddd' : 'F 2 2 -1d',
    'Fddd:1' : 'F 2 2 -1d',
    'Fddd1' : 'F 2 2 -1d',
    'FdddS' : 'F 2 2 -1d',
    'Fddd:2' : '-F 2uv 2vw',
    'Fddd2' : '-F 2uv 2vw',
    'FdddZ' : '-F 2uv 2vw',
    #  71
    'Immm' : '-I 2 2',
    'I2/m2/m2/m' : '-I 2 2',
    #  72
    'Ibam' : '-I 2 2c',
    'Imcb' : '-I 2a 2',
    'Icma' : '-I 2b 2b',
    #  73
    'Ibca' : '-I 2b 2c',
    'Icab' : '-I 2a 2b',
    #  74
    'Imma' : '-I 2b 2',
    'Immb' : '-I 2a 2a',
    'Ibmm' : '-I 2c 2c',
    'Icmm' : '-I 2 2b',
    'Imcm' : '-I 2 2a',
    'Imam' : '-I 2c 2',
    #  75
    'P4' : 'P 4',
    #  76
    'P41' : 'P 4w',
    #  77
    'P42' : 'P 4c',
    #  78
    'P43' : 'P 4cw',
    #  79
    'I4' : 'I 4',
    #  80
    'I41' : 'I 4bw',
    #  81
    'P-4' : 'P -4',
    #  82
    'I-4' : 'I -4',
    #  83
    'P4/m' : '-P 4',
    #  84
    'P42/m' : '-P 4c',
    #  85
    'P4/n' : 'P 4ab -1ab',
    'P4/n:1' : 'P 4ab -1ab',
    'P4/n1' : 'P 4ab -1ab',
    'P4/nS' : 'P 4ab -1ab',
    'P4/n:2' : '-P 4a',
    'P4/n2' : '-P 4a',
    'P4/nZ' : '-P 4a',
    #  86
    'P42/n' : 'P 4n -1n',
    'P42/n:1' : 'P 4n -1n',
    'P42/n1' : 'P 4n -1n',
    'P42/nS' : 'P 4n -1n',
    'P42/n:2' : '-P 4bc',
    'P42/n2' : '-P 4bc',
    'P42/nZ' : '-P 4bc',
    #  87
    'I4/m' : '-I 4',
    #  88
    'I41/a' : 'I 4bw -1bw',
    'I41/a:1' : 'I 4bw -1bw',
    'I41/a1' : 'I 4bw -1bw',
    'I41/aS' : 'I 4bw -1bw',
    'I41/a:2' : '-I 4ad',
    'I41/a2' : '-I 4ad',
    'I41/aZ' : '-I 4ad',
    #  89
    'P422' : 'P 4 2',
    #  90
    'P4212' : 'P 4ab 2ab',
    #  91
    'P4122' : 'P 4w 2c',
    #  92
    'P41212' : 'P 4abw 2nw',
    #  93
    'P4222' : 'P 4c 2',
    #  94
    'P42212' : 'P 4n 2n',
    #  95
    'P4322' : 'P 4cw 2c',
    #  96
    'P43212' : 'P 4nw 2abw',
    #  97
    'I422' : 'I 4 2',
    #  98
    'I4122' : 'I 4bw 2bw',
    #  99
    'P4mm' : 'P 4 -2',
    # 100
    'P4bm' : 'P 4 -2ab',
    # 101
    'P42cm' : 'P 4c -2c',
    # 102
    'P42nm' : 'P 4n -2n',
    # 103
    'P4cc' : 'P 4 -2c',
    # 104
    'P4nc' : 'P 4 -2n',
    # 105
    'P42mc' : 'P 4c -2',
    # 106
    'P42bc' : 'P 4c -2ab',
    # 107
    'I4mm' : 'I 4 -2',
    # 108
    'I4cm' : 'I 4 -2c',
    # 109
    'I41md' : 'I 4bw -2',
    # 110
    'I41cd' : 'I 4bw -2c',
    # 111
    'P-42m' : 'P -4 2',
    # 112
    'P-42c' : 'P -4 2c',
    # 113
    'P-421m' : 'P -4 2ab',
    # 114
    'P-421c' : 'P -4 2n',
    # 115
    'P-4m2' : 'P -4 -2',
    # 116
    'P-4c2' : 'P -4 -2c',
    # 117
    'P-4b2' : 'P -4 -2ab',
    # 118
    'P-4n2' : 'P -4 -2n',
    # 119
    'I-4m2' : 'I -4 -2',
    # 120
    'I-4c2' : 'I -4 -2c',
    # 121
    'I-42m' : 'I -4 2',
    # 122
    'I-42d' : 'I -4 2bw',
    # 123
    'P4/mmm' : '-P 4 2',
    'P4/m2/m2/m' : '-P 4 2',
    # 124
    'P4/mcc' : '-P 4 2c',
    # 125
    'P4/nbm' : 'P 4 2 -1ab',
    'P4/nbm:1' : 'P 4 2 -1ab',
    'P4/nbm1' : 'P 4 2 -1ab',
    'P4/nbmS' : 'P 4 2 -1ab',
    'P4/nbm:2' : '-P 4a 2b',
    'P4/nbm2' : '-P 4a 2b',
    'P4/nbmZ' : '-P 4a 2b',
    # 126
    'P4/nnc' : 'P 4 2 -1n',
    'P4/nnc:1' : 'P 4 2 -1n',
    'P4/nnc1' : 'P 4 2 -1n',
    'P4/nncS' : 'P 4 2 -1n',
    'P4/nnc:2' : '-P 4a 2bc',
    'P4/nnc2' : '-P 4a 2bc',
    'P4/nncZ' : '-P 4a 2bc',
    # 127
    'P4/mbm' : '-P 4 2ab',
    # 128
    'P4/mnc' : '-P 4 2n',
    # 129
    'P4/nmm' : 'P 4ab 2ab -1ab',
    'P4/nmm:1' : 'P 4ab 2ab -1ab',
    'P4/nmm1' : 'P 4ab 2ab -1ab',
    'P4/nmmS' : 'P 4ab 2ab -1ab',
    'P4/n21/m2/m(originchoice2)' : 'P 4ab 2ab -1ab',   # ? FINDSYM choice
    'P4/nmm:2' : '-P 4a 2a',
    'P4/nmm2' : '-P 4a 2a',
    'P4/nmmZ' : '-P 4a 2a',
    # 130
    'P4/ncc' : 'P 4ab 2n -1ab',
    'P4/ncc:1' : 'P 4ab 2n -1ab',
    'P4/ncc1' : 'P 4ab 2n -1ab',
    'P4/nccS' : 'P 4ab 2n -1ab',
    'P4/ncc:2' : '-P 4a 2ac',
    'P4/ncc2' : '-P 4a 2ac',
    'P4/nccZ' : '-P 4a 2ac',
    # 131
    'P42/mmc' : '-P 4c 2',
    # 132
    'P42/mcm' : '-P 4c 2c',
    # 133
    'P42/nbc' : 'P 4n 2c -1n',
    'P42/nbc:1' : 'P 4n 2c -1n',
    'P42/nbc1' : 'P 4n 2c -1n',
    'P42/nbcS' : 'P 4n 2c -1n',
    'P42/nbc:2' : '-P 4ac 2b',
    'P42/nbc2' : '-P 4ac 2b',
    'P42/nbcZ' : '-P 4ac 2b',
    # 134
    'P42/nnm' : 'P 4n 2 -1n',
    'P42/nnm:1' : 'P 4n 2 -1n',
    'P42/nnm1' : 'P 4n 2 -1n',
    'P42/nnmS' : 'P 4n 2 -1n',
    'P42/nnm:2' : '-P 4ac 2bc',
    'P42/nnm2' : '-P 4ac 2bc',
    'P42/nnmZ' : '-P 4ac 2bc',
    # 135
    'P42/mbc' : '-P 4c 2ab',
    # 136
    'P42/mnm' : '-P 4n 2n',
    # 137
    'P42/nmc' : 'P 4n 2n -1n',
    'P42/nmc:1' : 'P 4n 2n -1n',
    'P42/nmc1' : 'P 4n 2n -1n',
    'P42/nmcS' : 'P 4n 2n -1n',
    'P42/nmc:2' : '-P 4ac 2a',
    'P42/nmc2' : '-P 4ac 2a',
    'P42/nmcZ' : '-P 4ac 2a',
    # 138
    'P42/ncm' : 'P 4n 2ab -1n',
    'P42/ncm:1' : 'P 4n 2ab -1n',
    'P42/ncm1' : 'P 4n 2ab -1n',
    'P42/ncmS' : 'P 4n 2ab -1n',
    'P42/ncm:2' : '-P 4ac 2ac',
    'P42/ncm2' : '-P 4ac 2ac',
    'P42/ncmZ' : '-P 4ac 2ac',
    # 139
    'I4/mmm' : '-I 4 2',
    'I4/m2/m2/m' : '-I 4 2',
    # 140
    'I4/mcm' : '-I 4 2c',
    # 141
    'I41/amd' : 'I 4bw 2bw -1bw',
    'I41/amd:1' : 'I 4bw 2bw -1bw',
    'I41/amd1' : 'I 4bw 2bw -1bw',
    'I41/amdS' : 'I 4bw 2bw -1bw',
    'I41/amd:2' : '-I 4bd 2',
    'I41/amd2' : '-I 4bd 2',
    'I41/amdZ' : '-I 4bd 2',
    # 142
    'I41/acd' : 'I 4bw 2aw -1bw',
    'I41/acd:1' : 'I 4bw 2aw -1bw',
    'I41/acd1' : 'I 4bw 2aw -1bw',
    'I41/acdS' : 'I 4bw 2aw -1bw',
    'I41/acd:2' : '-I 4bd 2c',
    'I41/acd2' : '-I 4bd 2c',
    'I41/acdZ' : '-I 4bd 2c',
    # 143
    'P3' : 'P 3',
    # 144
    'P31' : 'P 31',
    # 145
    'P32' : 'P 32',
    # 146
    'R3' : 'R 3',
    'R3:H' : 'R 3',
    'R3H' : 'R 3',
    'R3:R' : 'P 3*',
    'R3R' : 'P 3*',
    # 147
    'P-3' : '-P 3',
    # 148
    'R-3' : '-R 3',
    'R-3:H' : '-R 3',
    'R-3H' : '-R 3',
    'R-3:R' : '-P 3*',
    'R-3R' : '-P 3*',
    # 149
    'P312' : 'P 3 2',
    # 150
    'P321' : 'P 3 2"',
    # 151
    'P3112' : 'P 31 2c (0 0 1)',
    # 152
    'P3121' : 'P 31 2"',
    # 153
    'P3212' : 'P 32 2c (0 0 -1)',
    # 154
    'P3221' : 'P 32 2"',
    # 155
    'R32' : 'R 3 2"',
    'R32:H' : 'R 3 2"',
    'R32H' : 'R 3 2"',
    'R32:R' : 'P 3* 2',
    'R32R' : 'P 3* 2',
    # 156
    'P3m1' : 'P 3 -2"',
    # 157
    'P31m' : 'P 3 -2',
    # 158
    'P3c1' : 'P 3 -2"c',
    # 159
    'P31c' : 'P 3 -2c',
    # 160
    'R3m' : 'R 3 -2"',
    'R3m:H' : 'R 3 -2"',
    'R3mH' : 'R 3 -2"',
    'R3m:R' : 'P 3* -2',
    'R3mR' : 'P 3* -2',
    'R3mHR' : 'T 3 -2"',
    # 161
    'R3c' : 'R 3 -2"c',
    'R3c:H' : 'R 3 -2"c',
    'R3cH' : 'R 3 -2"c',
    'R3c:R' : 'P 3* -2n',
    'R3cR' : 'P 3* -2n',
    # 162
    'P-31m' : '-P 3 2',
    # 163
    'P-31c' : '-P 3 2c',
    # 164
    'P-3m1' : '-P 3 2"',
    'P-32/m1' : '-P 3 2"',
    # 165
    'P-3c1' : '-P 3 2"c',
    # 166
    'R-3m' : '-R 3 2"',
    'R-32/m' : '-R 3 2"',
    'R-3m:H' : '-R 3 2"',
    'R-3mH' : '-R 3 2"',
    'R-32/m:H' : '-R 3 2"',
    'R-32/mH' : '-R 3 2"',
    'R-3m:R' : '-P 3* 2',
    'R-3mR' : '-P 3* 2',
    'R-32/m:R' : '-P 3* 2',
    'R-32/mR' : '-P 3* 2',
    'R-3mHR' : '-T 3 2"',
    # 167
    'R-3c' : '-R 3 2"c',
    'R-3c:H' : '-R 3 2"c',
    'R-3cH' : '-R 3 2"c',
    'R-3c:R' : '-P 3* 2n',
    'R-3cR' : '-P 3* 2n',
    # 168
    'P6' : 'P 6',
    # 169
    'P61' : 'P 61',
    # 170
    'P65' : 'P 65',
    # 171
    'P62' : 'P 62',
    # 172
    'P64' : 'P 64',
    # 173
    'P63' : 'P 6c',
    # 174
    'P-6' : 'P -6',
    # 175
    'P6/m' : '-P 6',
    # 176
    'P63/m' : '-P 6c',
    # 177
    'P622' : 'P 6 2',
    # 178
    'P6122' : 'P 61 2 (0 0 -1)',
    # 179
    'P6522' : 'P 65 2 (0 0 1)',
    # 180
    'P6222' : 'P 62 2c (0 0 1)',
    # 181
    'P6422' : 'P 64 2c (0 0 -1)',
    # 182
    'P6322' : 'P 6c 2c',
    # 183
    'P6mm' : 'P 6 -2',
    # 184
    'P6cc' : 'P 6 -2c',
    # 185
    'P63cm' : 'P 6c -2',
    # 186
    'P63mc' : 'P 6c -2c',
    # 187
    'P-6m2' : 'P -6 2',
    # 188
    'P-6c2' : 'P -6c 2',
    # 189
    'P-62m' : 'P -6 -2',
    # 190
    'P-62c' : 'P -6c -2c',
    # 191
    'P6/mmm' : '-P 6 2',
    'P6/m2/m2/m' : '-P 6 2',
    # 192
    'P6/mcc' : '-P 6 2c',
    # 193
    'P63/mcm' : '-P 6c 2',
    # 194
    'P63/mmc' : '-P 6c 2c',
    'P63/m2/m2/c' : '-P 6c 2c',
    # 195
    'P23' : 'P 2 2 3',
    # 196
    'F23' : 'F 2 2 3',
    # 197
    'I23' : 'I 2 2 3',
    # 198
    'P213' : 'P 2ac 2ab 3',
    # 199
    'I213' : 'I 2b 2c 3',
    # 200
    'Pm-3' : '-P 2 2 3',
    'P2/m-3' : '-P 2 2 3',
    'Pm3' : '-P 2 2 3',
    # 201
    'Pn-3' : 'P 2 2 3 -1n',
    'Pn-3:1' : 'P 2 2 3 -1n',
    'Pn-31' : 'P 2 2 3 -1n',
    'Pn-3S' : 'P 2 2 3 -1n',
    'Pn-3:2' : '-P 2ab 2bc 3',
    'Pn-32' : '-P 2ab 2bc 3',
    'Pn-3Z' : '-P 2ab 2bc 3',
    'Pn3' : 'P 2 2 3 -1n',
    # 202
    'Fm-3' : '-F 2 2 3',
    'F2/m-3' : '-F 2 2 3',
    'Fm3' : '-F 2 2 3',
    # 203
    'Fd-3' : 'F 2 2 3 -1d',
    'Fd-3:1' : 'F 2 2 3 -1d',
    'Fd-31' : 'F 2 2 3 -1d',
    'Fd-3S' : 'F 2 2 3 -1d',
    'Fd-3:2' : '-F 2uv 2vw 3',
    'Fd-32' : '-F 2uv 2vw 3',
    'Fd-3Z' : '-F 2uv 2vw 3',
    'Fd3' : 'F 2 2 3 -1d',
    # 204
    'Im-3' : '-I 2 2 3',
    'I2/m-3' : '-I 2 2 3',
    'Im3' : '-I 2 2 3',
    # 205
    'Pa-3' : '-P 2ac 2ab 3',
    'Pa3' : '-P 2ac 2ab 3',
    # 206
    'Ia-3' : '-I 2b 2c 3',
    'Ia3' : '-I 2b 2c 3',
    # 207
    'P432' : 'P 4 2 3',
    # 208
    'P4232' : 'P 4n 2 3',
    # 209
    'F432' : 'F 4 2 3',
    # 210
    'F4132' : 'F 4d 2 3',
    # 211
    'I432' : 'I 4 2 3',
    # 212
    'P4332' : 'P 4acd 2ab 3',
    # 213
    'P4132' : 'P 4bd 2ab 3',
    # 214
    'I4132' : 'I 4bd 2c 3',
    # 215
    'P-43m' : 'P -4 2 3',
    # 216
    'F-43m' : 'F -4 2 3',
    # 217
    'I-43m' : 'I -4 2 3',
    # 218
    'P-43n' : 'P -4n 2 3',
    # 219
    'F-43c' : 'F -4c 2 3',
    # 220
    'I-43d' : 'I -4bd 2c 3',
    # 221
    'Pm-3m' : '-P 4 2 3',
    'P4/m-32/m' : '-P 4 2 3',
    'Pm3m' : '-P 4 2 3',
    # 222
    'Pn-3n' : 'P 4 2 3 -1n',
    'Pn-3n:1' : 'P 4 2 3 -1n',
    'Pn-3n1' : 'P 4 2 3 -1n',
    'Pn-3nS' : 'P 4 2 3 -1n',
    'Pn-3n:2' : '-P 4a 2bc 3',
    'Pn-3n2' : '-P 4a 2bc 3',
    'Pn-3nZ' : '-P 4a 2bc 3',
    # 223
    'Pm-3n' : '-P 4n 2 3',
    'P2/m-3n' : '-P 4n 2 3',
    'Pm3n' : '-P 4n 2 3',
    # 224
    'Pn-3m' : 'P 4n 2 3 -1n',
    'Pn-3m:1' : 'P 4n 2 3 -1n',
    'Pn-3m1' : 'P 4n 2 3 -1n',
    'Pn-3mS' : 'P 4n 2 3 -1n',
    'Pn-3m:2' : '-P 4bc 2bc 3',
    'Pn-3m2' : '-P 4bc 2bc 3',
    'Pn-3mZ' : '-P 4bc 2bc 3',
    'Pn3m' : 'P 4n 2 3 -1n',
    # 225
    'Fm-3m' : '-F 4 2 3',
    'F4/m-32/m' : '-F 4 2 3',
    'Fm3m' : '-F 4 2 3',
    # 226
    'Fm-3c' : '-F 4c 2 3',
    'F2/m-3c' : '-F 4c 2 3',
    'Fm3c' : '-F 4c 2 3',
    # 227
    'Fd-3m' : 'F 4d 2 3 -1d',
    'Fd-3m:1' : 'F 4d 2 3 -1d',
    'Fd-3m1' : 'F 4d 2 3 -1d',
    'Fd-3mS' : 'F 4d 2 3 -1d',
    'Fd-3m:2' : '-F 4vw 2vw 3',
    'Fd-3m2' : '-F 4vw 2vw 3',
    'Fd-3mZ' : '-F 4vw 2vw 3',
    'Fd3m' : 'F 4d 2 3 -1d',
    # 228
    'Fd-3c' : 'F 4d 2 3 -1cd',
    'Fd-3c:1' : 'F 4d 2 3 -1cd',
    'Fd-3c1' : 'F 4d 2 3 -1cd',
    'Fd-3cS' : 'F 4d 2 3 -1cd',
    'Fd-3c:2' : '-F 4cvw 2vw 3',
    'Fd-3c2' : '-F 4cvw 2vw 3',
    'Fd-3cZ' : '-F 4cvw 2vw 3',
    'Fd3c' : 'F 4d 2 3 -1cd',
    # 229
    'Im-3m' : '-I 4 2 3',
    'I4/m-32/m' : '-I 4 2 3',
    'Im3m' : '-I 4 2 3',
    # 230
    'Ia-3d' : '-I 4bd 2c 3',
    'Ia3d' : '-I 4bd 2c 3',
    #######################
    # Non-standard settings
    # 1
    'A1' : 'A 1',
    'B1' : 'B 1',
    'C1' : 'C 1',
    'I1' : 'I 1',
    'F1' : 'F 1',
    # 2
    'A-1' : '-A 1',
    'B-1' : '-B 1',
    'C-1' : '-C 1',
    'I-1' : '-I 1',
    'F-1' : '-F 1',
    # 5
    'F112' : 'F 2',
    'F211' : 'F 2x',
    'F121' : 'F 2y',
    # 8
    'F11m' : 'F -2',
    'Fm11' : 'F -2x',
    'F1m1' : 'F -2y',
    # 9
    'F11d' : 'F -2d',
    'F1d1' : 'F -2yd',
    'Fd11' : 'F -2xd',
    # 12
    'F112/m' : '-F 2',
    'F2/m11' : '-F 2x',
    'F12/m1' : '-F 2y',
    # 15
    'F12/d1' : 'F 2ycuw -1c',
    # 70
    'Fddd' : '-F 2 2 -1d',
    'Fddd:1' : '-F 2 2 -1d',
    'Fddd1' : '-F 2 2 -1d',
    'FdddS' : '-F 2 2 -1d',
    'Fddd:2' : '-F 2uv 2vw',
    'Fddd2' : '-F 2uv 2vw',
    'FdddZ' : '-F 2uv 2vw',
    # 139
    'F4/m2/m2/m' : '-F 4 2',
    'F4/mmm' : '-F 4 2'
}

# Space group number for each Hall symbol
Hall2Number = {
    'Unknown' : 0,
    #   1
    'P 1' : 1,
    #   2
    '-P 1' : 2,
    #   3
    'P 2y' : 3,
    'P 2' : 3,
    'P 2x' : 3,
    #   4
    'P 2yb' : 4,
    'P 2c' : 4,
    'P 2xa' : 4,
    #   5
    'C 2y' : 5,
    'A 2y' : 5,
    'I 2y' : 5,
    'A 2' : 5,
    'B 2' : 5,
    'I 2' : 5,
    'B 2x' : 5,
    'C 2x' : 5,
    'I 2x' : 5,
    #   6
    'P -2y' : 6,
    'P -2' : 6,
    'P -2x' : 6,
    #   7
    'P -2yc' : 7,
    'P -2yac' : 7,
    'P -2ya' : 7,
    'P -2a' : 7,
    'P -2ab' : 7,
    'P -2b' : 7,
    'P -2xb' : 7,
    'P -2xbc' : 7,
    'P -2xc' : 7,
    #   8
    'C -2y' : 8,
    'A -2y' : 8,
    'I -2y' : 8,
    'A -2' : 8,
    'B -2' : 8,
    'I -2' : 8,
    'B -2x' : 8,
    'C -2x' : 8,
    'I -2x' : 8,
    #   9
    'C -2yc' : 9,
    'A -2yac' : 9,
    'I -2ya' : 9,
    'A -2ya' : 9,
    'C -2ybc' : 9,
    'I -2yc' : 9,
    'A -2a' : 9,
    'B -2bc' : 9,
    'I -2b' : 9,
    'B -2b' : 9,
    'A -2ac' : 9,
    'I -2a' : 9,
    'B -2xb' : 9,
    'C -2xbc' : 9,
    'I -2xc' : 9,
    'C -2xc' : 9,
    'B -2xbc' : 9,
    'I -2xb' : 9,
    #  10
    '-P 2y' : 10,
    '-P 2' : 10,
    '-P 2x' : 10,
    #  11
    '-P 2yb' : 11,
    '-P 2c' : 11,
    '-P 2xa' : 11,
    #  12
    '-C 2y' : 12,
    '-A 2y' : 12,
    '-I 2y' : 12,
    '-A 2' : 12,
    '-B 2' : 12,
    '-I 2' : 12,
    '-B 2x' : 12,
    '-C 2x' : 12,
    '-I 2x' : 12,
    #  13
    '-P 2yc' : 13,
    '-P 2yac' : 13,
    '-P 2ya' : 13,
    '-P 2a' : 13,
    '-P 2ab' : 13,
    '-P 2b' : 13,
    '-P 2xb' : 13,
    '-P 2xbc' : 13,
    '-P 2xc' : 13,
    #  14
    '-P 2ybc' : 14,
    '-P 2yn' : 14,
    '-P 2yab' : 14,
    '-P 2ac' : 14,
    '-P 2n' : 14,
    '-P 2bc' : 14,
    '-P 2xab' : 14,
    '-P 2xn' : 14,
    '-P 2xac' : 14,
    #  15
    '-C 2yc' : 15,
    '-A 2yac' : 15,
    '-I 2ya' : 15,
    '-A 2ya' : 15,
    '-C 2ybc' : 15,
    '-I 2yc' : 15,
    '-A 2a' : 15,
    '-B 2bc' : 15,
    '-I 2b' : 15,
    '-B 2b' : 15,
    '-A 2ac' : 15,
    '-I 2a' : 15,
    '-B 2xb' : 15,
    '-C 2xbc' : 15,
    '-I 2xc' : 15,
    '-C 2xc' : 15,
    '-B 2xbc' : 15,
    '-I 2xb' : 15,
    #  16
    'P 2 2' : 16,
    #  17
    'P 2c 2' : 17,
    'P 2a 2a' : 17,
    'P 2 2b' : 17,
    #  18
    'P 2 2ab' : 18,
    'P 2bc 2' : 18,
    'P 2ac 2ac' : 18,
    #  19
    'P 2ac 2ab' : 19,
    #  20
    'C 2c 2' : 20,
    'A 2a 2a' : 20,
    'B 2 2b' : 20,
    #  21
    'C 2 2' : 21,
    'A 2 2' : 21,
    'B 2 2' : 21,
    #  22
    'F 2 2' : 22,
    #  23
    'I 2 2' : 23,
    #  24
    'I 2b 2c' : 24,
    #  25
    'P 2 -2' : 25,
    'P -2 2' : 25,
    'P -2 -2' : 25,
    #  26
    'P 2c -2' : 26,
    'P 2c -2c' : 26,
    'P -2a 2a' : 26,
    'P -2 2a' : 26,
    'P -2 -2b' : 26,
    'P -2b -2' : 26,
    #  27
    'P 2 -2c' : 27,
    'P -2a 2' : 27,
    'P -2b -2b' : 27,
    #  28
    'P 2 -2a' : 28,
    'P 2 -2b' : 28,
    'P -2b 2' : 28,
    'P -2c 2' : 28,
    'P -2c -2c' : 28,
    'P -2a -2a' : 28,
    #  29
    'P 2c -2ac' : 29,
    'P 2c -2b' : 29,
    'P -2b 2a' : 29,
    'P -2ac 2a' : 29,
    'P -2bc -2c' : 29,
    'P -2a -2ab' : 29,
    #  30
    'P 2 -2bc' : 30,
    'P 2 -2ac' : 30,
    'P -2ac 2' : 30,
    'P -2ab 2' : 30,
    'P -2ab -2ab' : 30,
    'P -2bc -2bc' : 30,
    #  31
    'P 2ac -2' : 31,
    'P 2bc -2bc' : 31,
    'P -2ab 2ab' : 31,
    'P -2 2ac' : 31,
    'P -2 -2bc' : 31,
    'P -2ab -2' : 31,
    #  32
    'P 2 -2ab' : 32,
    'P -2bc 2' : 32,
    'P -2ac -2ac' : 32,
    #  33
    'P 2c -2n' : 33,
    'P 2c -2ab' : 33,
    'P -2bc 2a' : 33,
    'P -2n 2a' : 33,
    'P -2n -2ac' : 33,
    'P -2ac -2n' : 33,
    #  34
    'P 2 -2n' : 34,
    'P -2n 2' : 34,
    'P -2n -2n' : 34,
    #  35
    'C 2 -2' : 35,
    'A -2 2' : 35,
    'B -2 -2' : 35,
    #  36
    'C 2c -2' : 36,
    'C 2c -2c' : 36,
    'A -2a 2a' : 36,
    'A -2 2a' : 36,
    'B -2 -2b' : 36,
    'B -2b -2' : 36,
    #  37
    'C 2 -2c' : 37,
    'A -2a 2' : 37,
    'B -2b -2b' : 37,
    #  38
    'A 2 -2' : 38,
    'B 2 -2' : 38,
    'B -2 2' : 38,
    'C -2 2' : 38,
    'C -2 -2' : 38,
    'A -2 -2' : 38,
    #  39
    'A 2 -2c' : 39,
    'B 2 -2c' : 39,
    'B -2c 2' : 39,
    'C -2b 2' : 39,
    'C -2b -2b' : 39,
    'A -2c -2c' : 39,
    #  40
    'A 2 -2a' : 40,
    'B 2 -2b' : 40,
    'B -2b 2' : 40,
    'C -2c 2' : 40,
    'C -2c -2c' : 40,
    'A -2a -2a' : 40,
    #  41
    'A 2 -2ac' : 41,
    'B 2 -2bc' : 41,
    'B -2bc 2' : 41,
    'C -2bc 2' : 41,
    'C -2bc -2bc' : 41,
    'A -2ac -2ac' : 41,
    #  42
    'F 2 -2' : 42,
    'F -2 2' : 42,
    'F -2 -2' : 42,
    #  43
    'F 2 -2d' : 43,
    'F -2d 2' : 43,
    'F -2d -2d' : 43,
    #  44
    'I 2 -2' : 44,
    'I -2 2' : 44,
    'I -2 -2' : 44,
    #  45
    'I 2 -2c' : 45,
    'I -2a 2' : 45,
    'I -2b -2b' : 45,
    #  46
    'I 2 -2a' : 46,
    'I 2 -2b' : 46,
    'I -2b 2' : 46,
    'I -2c 2' : 46,
    'I -2c -2c' : 46,
    'I -2a -2a' : 46,
    #  47
    '-P 2 2' : 47,
    #  48
    'P 2 2 -1n' : 48,
    '-P 2ab 2bc' : 48,
    #  49
    '-P 2 2c' : 49,
    '-P 2a 2' : 49,
    '-P 2b 2b' : 49,
    #  50
    'P 2 2 -1ab' : 50,
    '-P 2ab 2b' : 50,
    'P 2 2 -1bc' : 50,
    '-P 2b 2bc' : 50,
    'P 2 2 -1ac' : 50,
    '-P 2a 2c' : 50,
    #  51
    '-P 2a 2a' : 51,
    '-P 2b 2' : 51,
    '-P 2 2b' : 51,
    '-P 2c 2c' : 51,
    '-P 2c 2' : 51,
    '-P 2 2a' : 51,
    #  52
    '-P 2a 2bc' : 52,
    '-P 2b 2n' : 52,
    '-P 2n 2b' : 52,
    '-P 2ab 2c' : 52,
    '-P 2ab 2n' : 52,
    '-P 2n 2bc' : 52,
    #  53
    '-P 2ac 2' : 53,
    '-P 2bc 2bc' : 53,
    '-P 2ab 2ab' : 53,
    '-P 2 2ac' : 53,
    '-P 2 2bc' : 53,
    '-P 2ab 2' : 53,
    #  54
    '-P 2a 2ac' : 54,
    '-P 2b 2c' : 54,
    '-P 2a 2b' : 54,
    '-P 2ac 2c' : 54,
    '-P 2bc 2b' : 54,
    '-P 2b 2ab' : 54,
    #  55
    '-P 2 2ab' : 55,
    '-P 2bc 2' : 55,
    '-P 2ac 2ac' : 55,
    #  56
    '-P 2ab 2ac' : 56,
    '-P 2ac 2bc' : 56,
    '-P 2bc 2ab' : 56,
    #  57
    '-P 2c 2b' : 57,
    '-P 2c 2ac' : 57,
    '-P 2ac 2a' : 57,
    '-P 2b 2a' : 57,
    '-P 2a 2ab' : 57,
    '-P 2bc 2c' : 57,
    #  58
    '-P 2 2n' : 58,
    '-P 2n 2' : 58,
    '-P 2n 2n' : 58,
    #  59
    'P 2 2ab -1ab' : 59,
    '-P 2ab 2a' : 59,
    'P 2bc 2 -1bc' : 59,
    '-P 2c 2bc' : 59,
    'P 2ac 2ac -1ac' : 59,
    '-P 2c 2a' : 59,
    #  60
    '-P 2n 2ab' : 60,
    '-P 2n 2c' : 60,
    '-P 2a 2n' : 60,
    '-P 2bc 2n' : 60,
    '-P 2ac 2b' : 60,
    '-P 2b 2ac' : 60,
    #  61
    '-P 2ac 2ab' : 61,
    '-P 2bc 2ac' : 61,
    #  62
    '-P 2ac 2n' : 62,
    '-P 2bc 2a' : 62,
    '-P 2c 2ab' : 62,
    '-P 2n 2ac' : 62,
    '-P 2n 2a' : 62,
    '-P 2c 2n' : 62,
    #  63
    '-C 2c 2' : 63,
    '-C 2c 2c' : 63,
    '-A 2a 2a' : 63,
    '-A 2 2a' : 63,
    '-B 2 2b' : 63,
    '-B 2b 2' : 63,
    #  64
    '-C 2bc 2' : 64,
    '-C 2bc 2bc' : 64,
    '-A 2ac 2ac' : 64,
    '-A 2 2ac' : 64,
    '-B 2 2bc' : 64,
    '-B 2bc 2' : 64,
    #  65
    '-C 2 2' : 65,
    '-A 2 2' : 65,
    '-B 2 2' : 65,
    #  66
    '-C 2 2c' : 66,
    '-A 2a 2' : 66,
    '-B 2b 2b' : 66,
    #  67
    '-C 2b 2' : 67,
    '-C 2b 2b' : 67,
    '-A 2c 2c' : 67,
    '-A 2 2c' : 67,
    '-B 2 2c' : 67,
    '-B 2c 2' : 67,
    #  68
    'C 2 2 -1bc' : 68,
    '-C 2b 2bc' : 68,
    'C 2 2 -1bc' : 68,
    '-C 2b 2c' : 68,
    'A 2 2 -1ac' : 68,
    '-A 2a 2c' : 68,
    'A 2 2 -1ac' : 68,
    '-A 2ac 2c' : 68,
    'B 2 2 -1bc' : 68,
    '-B 2bc 2b' : 68,
    'B 2 2 -1bc' : 68,
    '-B 2b 2bc' : 68,
    #  69
    '-F 2 2' : 69,
    #  70
    'F 2 2 -1d' : 70,
    '-F 2uv 2vw' : 70,
    #  71
    '-I 2 2' : 71,
    #  72
    '-I 2 2c' : 72,
    '-I 2a 2' : 72,
    '-I 2b 2b' : 72,
    #  73
    '-I 2b 2c' : 73,
    '-I 2a 2b' : 73,
    #  74
    '-I 2b 2' : 74,
    '-I 2a 2a' : 74,
    '-I 2c 2c' : 74,
    '-I 2 2b' : 74,
    '-I 2 2a' : 74,
    '-I 2c 2' : 74,
    #  75
    'P 4' : 75,
    #  76
    'P 4w' : 76,
    #  77
    'P 4c' : 77,
    #  78
    'P 4cw' : 78,
    #  79
    'I 4' : 79,
    #  80
    'I 4bw' : 80,
    #  81
    'P -4' : 81,
    #  82
    'I -4' : 82,
    #  83
    '-P 4' : 83,
    #  84
    '-P 4c' : 84,
    #  85
    'P 4ab -1ab' : 85,
    '-P 4a' : 85,
    #  86
    'P 4n -1n' : 86,
    '-P 4bc' : 86,
    #  87
    '-I 4' : 87,
    #  88
    'I 4bw -1bw' : 88,
    '-I 4ad' : 88,
    #  89
    'P 4 2' : 89,
    #  90
    'P 4ab 2ab' : 90,
    #  91
    'P 4w 2c' : 91,
    #  92
    'P 4abw 2nw' : 92,
    #  93
    'P 4c 2' : 93,
    #  94
    'P 4n 2n' : 94,
    #  95
    'P 4cw 2c' : 95,
    #  96
    'P 4nw 2abw' : 96,
    #  97
    'I 4 2' : 97,
    #  98
    'I 4bw 2bw' : 98,
    #  99
    'P 4 -2' : 99,
    # 100
    'P 4 -2ab' : 100,
    # 101
    'P 4c -2c' : 101,
    # 102
    'P 4n -2n' : 102,
    # 103
    'P 4 -2c' : 103,
    # 104
    'P 4 -2n' : 104,
    # 105
    'P 4c -2' : 105,
    # 106
    'P 4c -2ab' : 106,
    # 107
    'I 4 -2' : 107,
    # 108
    'I 4 -2c' : 108,
    # 109
    'I 4bw -2' : 109,
    # 110
    'I 4bw -2c' : 110,
    # 111
    'P -4 2' : 111,
    # 112
    'P -4 2c' : 112,
    # 113
    'P -4 2ab' : 113,
    # 114
    'P -4 2n' : 114,
    # 115
    'P -4 -2' : 115,
    # 116
    'P -4 -2c' : 116,
    # 117
    'P -4 -2ab' : 117,
    # 118
    'P -4 -2n' : 118,
    # 119
    'I -4 -2' : 119,
    # 120
    'I -4 -2c' : 120,
    # 121
    'I -4 2' : 121,
    # 122
    'I -4 2bw' : 122,
    # 123
    '-P 4 2' : 123,
    # 124
    '-P 4 2c' : 124,
    # 125
    'P 4 2 -1ab' : 125,
    '-P 4a 2b' : 125,
    # 126
    'P 4 2 -1n' : 126,
    '-P 4a 2bc' : 126,
    # 127
    '-P 4 2ab' : 127,
    # 128
    '-P 4 2n' : 128,
    # 129
    'P 4ab 2ab -1ab' : 129,
    '-P 4a 2a' : 129,
    # 130
    'P 4ab 2n -1ab' : 130,
    '-P 4a 2ac' : 130,
    # 131
    '-P 4c 2' : 131,
    # 132
    '-P 4c 2c' : 132,
    # 133
    'P 4n 2c -1n' : 133,
    '-P 4ac 2b' : 133,
    # 134
    'P 4n 2 -1n' : 134,
    '-P 4ac 2bc' : 134,
    # 135
    '-P 4c 2ab' : 135,
    # 136
    '-P 4n 2n' : 136,
    # 137
    'P 4n 2n -1n' : 137,
    '-P 4ac 2a' : 137,
    # 138
    'P 4n 2ab -1n' : 138,
    '-P 4ac 2ac' : 138,
    # 139
    '-I 4 2' : 139,
    # 140
    '-I 4 2c' : 140,
    # 141
    'I 4bw 2bw -1bw' : 141,
    '-I 4bd 2' : 141,
    # 142
    'I 4bw 2aw -1bw' : 142,
    '-I 4bd 2c' : 142,
    # 143
    'P 3' : 143,
    # 144
    'P 31' : 144,
    # 145
    'P 32' : 145,
    # 146
    'R 3' : 146,
    'P 3*' : 146,
    # 147
    '-P 3' : 147,
    # 148
    '-R 3' : 148,
    '-P 3*' : 148,
    # 149
    'P 3 2' : 149,
    # 150
    'P 3 2"' : 150,
    # 151
    'P 31 2c (0 0 1)' : 151,
    # 152
    'P 31 2"' : 152,
    # 153
    'P 32 2c (0 0 -1)' : 153,
    # 154
    'P 32 2"' : 154,
    # 155
    'R 3 2"' : 155,
    'P 3* 2' : 155,
    # 156
    'P 3 -2"' : 156,
    # 157
    'P 3 -2' : 157,
    # 158
    'P 3 -2"c' : 158,
    # 159
    'P 3 -2c' : 159,
    # 160
    'R 3 -2"' : 160,
    'P 3* -2' : 160,
    # 161
    'R 3 -2"c' : 161,
    'P 3* -2n' : 161,
    # 162
    '-P 3 2' : 162,
    # 163
    '-P 3 2c' : 163,
    # 164
    '-P 3 2"' : 164,
    # 165
    '-P 3 2"c' : 165,
    # 166
    '-R 3 2"' : 166,
    '-P 3* 2' : 166,
    # 167
    '-R 3 2"c' : 167,
    '-P 3* 2n' : 167,
    # 168
    'P 6' : 168,
    # 169
    'P 61' : 169,
    # 170
    'P 65' : 170,
    # 171
    'P 62' : 171,
    # 172
    'P 64' : 172,
    # 173
    'P 6c' : 173,
    # 174
    'P -6' : 174,
    # 175
    '-P 6' : 175,
    # 176
    '-P 6c' : 176,
    # 177
    'P 6 2' : 177,
    # 178
    'P 61 2 (0 0 -1)' : 178,
    # 179
    'P 65 2 (0 0 1)' : 179,
    # 180
    'P 62 2c (0 0 1)' : 180,
    # 181
    'P 64 2c (0 0 -1)' : 181,
    # 182
    'P 6c 2c' : 182,
    # 183
    'P 6 -2' : 183,
    # 184
    'P 6 -2c' : 184,
    # 185
    'P 6c -2' : 185,
    # 186
    'P 6c -2c' : 186,
    # 187
    'P -6 2' : 187,
    # 188
    'P -6c 2' : 188,
    # 189
    'P -6 -2' : 189,
    # 190
    'P -6c -2c' : 190,
    # 191
    '-P 6 2' : 191,
    # 192
    '-P 6 2c' : 192,
    # 193
    '-P 6c 2' : 193,
    # 194
    '-P 6c 2c' : 194,
    # 195
    'P 2 2 3' : 195,
    # 196
    'F 2 2 3' : 196,
    # 197
    'I 2 2 3' : 197,
    # 198
    'P 2ac 2ab 3' : 198,
    # 199
    'I 2b 2c 3' : 199,
    # 200
    '-P 2 2 3' : 200,
    # 201
    'P 2 2 3 -1n' : 201,
    '-P 2ab 2bc 3' : 201,
    # 202
    '-F 2 2 3' : 202,
    # 203
    'F 2 2 3 -1d' : 203,
    '-F 2uv 2vw 3' : 203,
    # 204
    '-I 2 2 3' : 204,
    # 205
    '-P 2ac 2ab 3' : 205,
    # 206
    '-I 2b 2c 3' : 206,
    # 207
    'P 4 2 3' : 207,
    # 208
    'P 4n 2 3' : 208,
    # 209
    'F 4 2 3' : 209,
    # 210
    'F 4d 2 3' : 210,
    # 211
    'I 4 2 3' : 211,
    # 212
    'P 4acd 2ab 3' : 212,
    # 213
    'P 4bd 2ab 3' : 213,
    # 214
    'I 4bd 2c 3' : 214,
    # 215
    'P -4 2 3' : 215,
    # 216
    'F -4 2 3' : 216,
    # 217
    'I -4 2 3' : 217,
    # 218
    'P -4n 2 3' : 218,
    # 219
    'F -4c 2 3' : 219,
    # 220
    'I -4bd 2c 3' : 220,
    # 221
    '-P 4 2 3' : 221,
    # 222
    'P 4 2 3 -1n' : 222,
    '-P 4a 2bc 3' : 222,
    # 223
    '-P 4n 2 3' : 223,
    # 224
    'P 4n 2 3 -1n' : 224,
    '-P 4bc 2bc 3' : 224,
    # 225
    '-F 4 2 3' : 225,
    # 226
    '-F 4c 2 3' : 226,
    # 227
    'F 4d 2 3 -1d' : 227,
    '-F 4vw 2vw 3' : 227,
    # 228
    'F 4d 2 3 -1cd' : 228,
    '-F 4cvw 2vw 3' : 228,
    # 229
    '-I 4 2 3' : 229,
    # 230
    '-I 4bd 2c 3' : 230,
    #######################
    # Non-standard settings
    # 1
    'A 1' : 1,
    'B 1' : 1,
    'C 1' : 1,
    'I 1' : 1,
    'F 1' : 1,
    # 2
    '-A 1' : 2,
    '-B 1' : 2,
    '-C 1' : 2,
    '-I 1' : 2,
    '-F 1' : 2,
    # 5
    'F 2' : 5,
    'F 2x' : 5,
    'F 2y' : 5,
    # 8
    'F -2' : 8,
    'F -2x' : 8,
    'F -2y' : 8,
    # 9
    'F -2d' : 9,
    'F -2yd' : 9,
    'F -2xd' : 9,
    # 12
    '-F 2' : 12,
    '-F 2x' : 12,
    '-F 2y' : 12,
    # 15
    'F 2ycuw -1c' : 15,
    # 70
    '-F 2 2 -1d' : 70,
    '-F 2uv 2vw' : 70,
    # 139
    '-F 4 2' : 139
    }

# The space groups that has only one possible "standard" setting
Number2Hall = { 1 : 'P 1',
                2 : '-P 1',
                16 : 'P 2 2',
                19 : 'P 2ac 2ab',
                22 : 'F 2 2',
                23 : 'I 2 2',
                24 : 'I 2b 2c',
                47 : '-P 2 2',
                69 : '-F 2 2',
                71 : '-I 2 2',
                75 : 'P 4',
                76 : 'P 4w',
                77 : 'P 4c',
                78 : 'P 4cw',
                79 : 'I 4',
                80 : 'I 4bw',
                81 : 'P -4',
                82 : 'I -4',
                83 : '-P 4',
                84 : '-P 4c',
                87 : '-I 4',
                89 : 'P 4 2',
                90 : 'P 4ab 2ab',
                91 : 'P 4w 2c',
                92 : 'P 4abw 2nw',
                93 : 'P 4c 2',
                94 : 'P 4n 2n',
                95 : 'P 4cw 2c',
                96 : 'P 4nw 2abw',
                97 : 'I 4 2',
                98 : 'I 4bw 2bw',
                99 : 'P 4 -2',
                100 : 'P 4 -2ab',
                101 : 'P 4c -2c',
                102 : 'P 4n -2n',
                103 : 'P 4 -2c',
                104 : 'P 4 -2n',
                105 : 'P 4c -2',
                106 : 'P 4c -2ab',
                107 : 'I 4 -2',
                108 : 'I 4 -2c',
                109 : 'I 4bw -2',
                110 : 'I 4bw -2c',
                111 : 'P -4 2',
                112 : 'P -4 2c',
                113 : 'P -4 2ab',
                114 : 'P -4 2n',
                115 : 'P -4 -2',
                116 : 'P -4 -2c',
                117 : 'P -4 -2ab',
                118 : 'P -4 -2n',
                119 : 'I -4 -2',
                120 : 'I -4 -2c',
                121 : 'I -4 2',
                122 : 'I -4 2bw',
                123 : '-P 4 2',
                124 : '-P 4 2c',
                127 : '-P 4 2ab',
                128 : '-P 4 2n',
                131 : '-P 4c 2',
                132 : '-P 4c 2c',
                135 : '-P 4c 2ab',
                136 : '-P 4n 2n',
                139 : '-I 4 2',
                140 : '-I 4 2c',
                143 : 'P 3',
                144 : 'P 31',
                145 : 'P 32',
                147 : '-P 3',
                149 : 'P 3 2',
                150 : 'P 3 2"',
                151 : 'P 31 2c (0 0 1)',
                152 : 'P 31 2"',
                153 : 'P 32 2c (0 0 -1)',
                154 : 'P 32 2"',
                156 : 'P 3 -2"',
                157 : 'P 3 -2',
                158 : 'P 3 -2"c',
                159 : 'P 3 -2c',
                162 : '-P 3 2',
                163 : '-P 3 2c',
                164 : '-P 3 2"',
                165 : '-P 3 2"c',
                168 : 'P 6',
                169 : 'P 61',
                170 : 'P 65',
                171 : 'P 62',
                172 : 'P 64',
                173 : 'P 6c',
                174 : 'P -6',
                175 : '-P 6',
                176 : '-P 6c',
                177 : 'P 6 2',
                178 : 'P 61 2 (0 0 -1)',
                179 : 'P 65 2 (0 0 1)',
                180 : 'P 62 2c (0 0 1)',
                181 : 'P 64 2c (0 0 -1)',
                182 : 'P 6c 2c',
                183 : 'P 6 -2',
                184 : 'P 6 -2c',
                185 : 'P 6c -2',
                186 : 'P 6c -2c',
                187 : 'P -6 2',
                188 : 'P -6c 2',
                189 : 'P -6 -2',
                190 : 'P -6c -2c',
                191 : '-P 6 2',
                192 : '-P 6 2c',
                193 : '-P 6c 2',
                194 : '-P 6c 2c',
                195 : 'P 2 2 3',
                196 : 'F 2 2 3',
                197 : 'I 2 2 3',
                198 : 'P 2ac 2ab 3',
                199 : 'I 2b 2c 3',
                200 : '-P 2 2 3',
                202 : '-F 2 2 3',
                204 : '-I 2 2 3',
                205 : '-P 2ac 2ab 3',
                206 : '-I 2b 2c 3',
                207 : 'P 4 2 3',
                208 : 'P 4n 2 3',
                209 : 'F 4 2 3',
                210 : 'F 4d 2 3',
                211 : 'I 4 2 3',
                212 : 'P 4acd 2a 3',
                213 : 'P 4bd 2ab 3',
                214 : 'I 4bd 2c 3',
                215 : 'P -4 2 3',
                216 : 'F -4 2 3',
                217 : 'I -4 2 3',
                218 : 'P -4n 2 3',
                219 : 'F -4c 2 3',
                220 : 'I -4bd 2c 3',
                221 : '-P 4 2 3',
                223 : '-P 4n 2 3',
                225 : '-F 4 2 3',
                226 : '-F 4c 2 3',
                229 : '-I 4 2 3',
                230 : '-I 4bd 2c 3'
                }

Hall2HM = {
    'Unknown' : 'Unknown',
    #   1
    'P 1' : 'P1',
    #   2
    '-P 1' : 'P-1',
    #   3
    'P 2y' : 'P121',
    'P 2' : 'P112',
    'P 2x' : 'P211',
    #   4
    'P 2yb' : 'P1211',
    'P 2c' : 'P1121',
    'P 2xa' : 'P2111',
    #   5
    'C 2y' : 'C121',
    'A 2y' : 'A121',
    'I 2y' : 'I121',
    'A 2' : 'A112',
    'B 2' : 'B112',
    'I 2' : 'I112',
    'B 2x' : 'B211',
    'C 2x' : 'C211',
    'I 2x' : 'I211',
    #   6
    'P -2y' : 'P1m1',
    'P -2' : 'P11m',
    'P -2x' : 'Pm11',
    #   7
    'P -2yc' : 'P1c1',
    'P -2yac' : 'P1n1',
    'P -2ya' : 'P1a1',
    'P -2a' : 'P11a',
    'P -2ab' : 'P11n',
    'P -2b' : 'P11b',
    'P -2xb' : 'Pb11',
    'P -2xbc' : 'Pn11',
    'P -2xc' : 'Pc11',
    #   8
    'C -2y' : 'C1m1',
    'A -2y' : 'A1m1',
    'I -2y' : 'I1m1',
    'A -2' : 'A11m',
    'B -2' : 'B11m',
    'I -2' : 'I11m',
    'B -2x' : 'Bm11',
    'C -2x' : 'Cm11',
    'I -2x' : 'Im11',
    #   9
    'C -2yc' : 'C1c1',
    'A -2yac' : 'A1n1',
    'I -2ya' : 'I1a1',
    'A -2ya' : 'A1a1',
    'C -2ybc' : 'C1n1',
    'I -2yc' : 'I1c1',
    'A -2a' : 'A11a',
    'B -2bc' : 'B11n',
    'I -2b' : 'I11b',
    'B -2b' : 'B11b',
    'A -2ac' : 'A11n',
    'I -2a' : 'I11a',
    'B -2xb' : 'Bb11',
    'C -2xbc' : 'Cn11',
    'I -2xc' : 'Ic11',
    'C -2xc' : 'Cc11',
    'B -2xbc' : 'Bn11',
    'I -2xb' : 'Ib11',
    #  10
    '-P 2y' : 'P12/m1',
    '-P 2' : 'P112/m',
    '-P 2x' : 'P2/m11',
    #  11
    '-P 2yb' : 'P121/m1',
    '-P 2c' : 'P1121/m',
    '-P 2xa' : 'P21/m11',
    #  12
    '-C 2y' : 'C12/m1',
    '-A 2y' : 'A12/m1',
    '-I 2y' : 'I12/m1',
    '-A 2' : 'A112/m',
    '-B 2' : 'B112/m',
    '-I 2' : 'I112/m',
    '-B 2x' : 'B2/m11',
    '-C 2x' : 'C2/m11',
    '-I 2x' : 'I2/m11',
    #  13
    '-P 2yc' : 'P12/c1',
    '-P 2yac' : 'P12/n1',
    '-P 2ya' : 'P12/a1',
    '-P 2a' : 'P112/a',
    '-P 2ab' : 'P112/n',
    '-P 2b' : 'P112/b',
    '-P 2xb' : 'P2/b11',
    '-P 2xbc' : 'P2/n11',
    '-P 2xc' : 'P2/c11',
    #  14
    '-P 2ybc' : 'P121/c1',
    '-P 2yn' : 'P121/n1',
    '-P 2yab' : 'P121/a1',
    '-P 2ac' : 'P1121/a',
    '-P 2n' : 'P1121/n',
    '-P 2bc' : 'P1121/b',
    '-P 2xab' : 'P21/b11',
    '-P 2xn' : 'P21/n11',
    '-P 2xac' : 'P21/c11',
    #  15
    '-C 2yc' : 'C12/c1',
    '-A 2yac' : 'A12/n1',
    '-I 2ya' : 'I12/a1',
    '-A 2ya' : 'A12/a1',
    '-C 2ybc' : 'C12/n1',
    '-I 2yc' : 'I12/c1',
    '-A 2a' : 'A112/a',
    '-B 2bc' : 'B112/n',
    '-I 2b' : 'I112/b',
    '-B 2b' : 'B112/b',
    '-A 2ac' : 'A112/n',
    '-I 2a' : 'I112/a',
    '-B 2xb' : 'B2/b11',
    '-C 2xbc' : 'C2/n11',
    '-I 2xc' : 'I2/c11',
    '-C 2xc' : 'C2/c11',
    '-B 2xbc' : 'B2/n11',
    '-I 2xb' : 'I2/b11',
    #  16
    'P 2 2' : 'P222',
    #  17
    'P 2c 2' : 'P2221',
    'P 2a 2a' : 'P2122',
    'P 2 2b' : 'P2212',
    #  18
    'P 2 2ab' : 'P21212',
    'P 2bc 2' : 'P22121',
    'P 2ac 2ac' : 'P21221',
    #  19
    'P 2ac 2ab' : 'P212121',
    #  20
    'C 2c 2' : 'C2221',
    'A 2a 2a' : 'A2122',
    'B 2 2b' : 'B2212',
    #  21
    'C 2 2' : 'C222',
    'A 2 2' : 'A222',
    'B 2 2' : 'B222',
    #  22
    'F 2 2' : 'F222',
    #  23
    'I 2 2' : 'I222',
    #  24
    'I 2b 2c' : 'I212121',
    #  25
    'P 2 -2' : 'Pmm2',
    'P -2 2' : 'P2mm',
    'P -2 -2' : 'Pm2m',
    #  26
    'P 2c -2' : 'Pmc21',
    'P 2c -2c' : 'Pcm21',
    'P -2a 2a' : 'P21ma',
    'P -2 2a' : 'P21am',
    'P -2 -2b' : 'Pb21m',
    'P -2b -2' : 'Pm21b',
    #  27
    'P 2 -2c' : 'Pcc2',
    'P -2a 2' : 'P2aa',
    'P -2b -2b' : 'Pb2b',
    #  28
    'P 2 -2a' : 'Pma2',
    'P 2 -2b' : 'Pbm2',
    'P -2b 2' : 'P2mb',
    'P -2c 2' : 'P2cm',
    'P -2c -2c' : 'Pc2m',
    'P -2a -2a' : 'Pm2a',
    #  29
    'P 2c -2ac' : 'Pca21',
    'P 2c -2b' : 'Pbc21',
    'P -2b 2a' : 'P21ab',
    'P -2ac 2a' : 'P21ca',
    'P -2bc -2c' : 'Pc21b',
    'P -2a -2ab' : 'Pb21a',
    #  30
    'P 2 -2bc' : 'Pnc2',
    'P 2 -2ac' : 'Pcn2',
    'P -2ac 2' : 'P2na',
    'P -2ab 2' : 'P2an',
    'P -2ab -2ab' : 'Pb2n',
    'P -2bc -2bc' : 'Pn2b',
    #  31
    'P 2ac -2' : 'Pmn21',
    'P 2bc -2bc' : 'Pnm21',
    'P -2ab 2ab' : 'P21mn',
    'P -2 2ac' : 'P21nm',
    'P -2 -2bc' : 'Pn21m',
    'P -2ab -2' : 'Pm21n',
    #  32
    'P 2 -2ab' : 'Pba2',
    'P -2bc 2' : 'P2cb',
    'P -2ac -2ac' : 'Pc2a',
    #  33
    'P 2c -2n' : 'Pna21',
    'P 2c -2ab' : 'Pbn21',
    'P -2bc 2a' : 'P21nb',
    'P -2n 2a' : 'P21cn',
    'P -2n -2ac' : 'Pc21n',
    'P -2ac -2n' : 'Pn21a',
    #  34
    'P 2 -2n' : 'Pnn2',
    'P -2n 2' : 'P2nn',
    'P -2n -2n' : 'Pn2n',
    #  35
    'C 2 -2' : 'Cmm2',
    'A -2 2' : 'A2mm',
    'B -2 -2' : 'Bm2m',
    #  36
    'C 2c -2' : 'Cmc21',
    'C 2c -2c' : 'Ccm21',
    'A -2a 2a' : 'A21ma',
    'A -2 2a' : 'A21am',
    'B -2 -2b' : 'Bb21m',
    'B -2b -2' : 'Bm21b',
    #  37
    'C 2 -2c' : 'Ccc2',
    'A -2a 2' : 'A2aa',
    'B -2b -2b' : 'Bb2b',
    #  38
    'A 2 -2' : 'Amm2',
    'B 2 -2' : 'Bmm2',
    'B -2 2' : 'B2mm',
    'C -2 2' : 'C2mm',
    'C -2 -2' : 'Cm2m',
    'A -2 -2' : 'Am2m',
    #  39
    'A 2 -2c' : 'Abm2',
    'B 2 -2c' : 'Bma2',
    'B -2c 2' : 'B2cm',
    'C -2b 2' : 'C2mb',
    'C -2b -2b' : 'Cm2a',
    'A -2c -2c' : 'Ac2m',
    #  40
    'A 2 -2a' : 'Ama2',
    'B 2 -2b' : 'Bbm2',
    'B -2b 2' : 'B2mb',
    'C -2c 2' : 'C2cm',
    'C -2c -2c' : 'Cc2m',
    'A -2a -2a' : 'Am2a',
    #  41
    'A 2 -2ac' : 'Aba2',
    'B 2 -2bc' : 'Bba2',
    'B -2bc 2' : 'B2cb',
    'C -2bc 2' : 'C2cb',
    'C -2bc -2bc' : 'Cc2a',
    'A -2ac -2ac' : 'Ac2a',
    #  42
    'F 2 -2' : 'Fmm2',
    'F -2 2' : 'F2mm',
    'F -2 -2' : 'Fm2m',
    #  43
    'F 2 -2d' : 'Fdd2',
    'F -2d 2' : 'F2dd',
    'F -2d -2d' : 'Fd2d',
    #  44
    'I 2 -2' : 'Imm2',
    'I -2 2' : 'I2mm',
    'I -2 -2' : 'Im2m',
    #  45
    'I 2 -2c' : 'Iba2',
    'I -2a 2' : 'I2cb',
    'I -2b -2b' : 'Ic2a',
    #  46
    'I 2 -2a' : 'Ima2',
    'I 2 -2b' : 'Ibm2',
    'I -2b 2' : 'I2mb',
    'I -2c 2' : 'I2cm',
    'I -2c -2c' : 'Ic2m',
    'I -2a -2a' : 'Im2a',
    #  47
    '-P 2 2' : 'Pmmm',
    #  48
    'P 2 2 -1n' : 'Pnnn:1',
    '-P 2ab 2bc' : 'Pnnn:2',
    #  49
    '-P 2 2c' : 'Pccm',
    '-P 2a 2' : 'Pmaa',
    '-P 2b 2b' : 'Pbmb',
    #  50
    'P 2 2 -1ab' : 'Pban:1',
    '-P 2ab 2b' : 'Pban:2',
    'P 2 2 -1bc' : 'Pncb:1',
    '-P 2b 2bc' : 'Pncb:2',
    'P 2 2 -1ac' : 'Pcna:1',
    '-P 2a 2c' : 'Pcna:2',
    #  51
    '-P 2a 2a' : 'Pmma',
    '-P 2b 2' : 'Pmmb',
    '-P 2 2b' : 'Pbmm',
    '-P 2c 2c' : 'Pcmm',
    '-P 2c 2' : 'Pmcm',
    '-P 2 2a' : 'Pmam',
    #  52
    '-P 2a 2bc' : 'Pnna',
    '-P 2b 2n' : 'Pnnb',
    '-P 2n 2b' : 'Pbnn',
    '-P 2ab 2c' : 'Pcnn',
    '-P 2ab 2n' : 'Pncn',
    '-P 2n 2bc' : 'Pnan',
    #  53
    '-P 2ac 2' : 'Pmna',
    '-P 2bc 2bc' : 'Pnmb',
    '-P 2ab 2ab' : 'Pbmn',
    '-P 2 2ac' : 'Pcnm',
    '-P 2 2bc' : 'Pncm',
    '-P 2ab 2' : 'Pman',
    #  54
    '-P 2a 2ac' : 'Pcca',
    '-P 2b 2c' : 'Pccb',
    '-P 2a 2b' : 'Pbaa',
    '-P 2ac 2c' : 'Pcaa',
    '-P 2bc 2b' : 'Pbcb',
    '-P 2b 2ab' : 'Pbab',
    #  55
    '-P 2 2ab' : 'Pbam',
    '-P 2bc 2' : 'Pmcb',
    '-P 2ac 2ac' : 'Pcma',
    #  56
    '-P 2ab 2ac' : 'Pccn',
    '-P 2ac 2bc' : 'Pnaa',
    '-P 2bc 2ab' : 'Pbnb',
    #  57
    '-P 2c 2b' : 'Pbcm',
    '-P 2c 2ac' : 'Pcam',
    '-P 2ac 2a' : 'Pmca',
    '-P 2b 2a' : 'Pmab',
    '-P 2a 2ab' : 'Pbma',
    '-P 2bc 2c' : 'Pcmb',
    #  58
    '-P 2 2n' : 'Pnnm',
    '-P 2n 2' : 'Pmnn',
    '-P 2n 2n' : 'Pnmn',
    #  59
    'P 2 2ab -1ab' : 'Pmmn:1',
    '-P 2ab 2a' : 'Pmmn:2',
    'P 2bc 2 -1bc' : 'Pnmm:1',
    '-P 2c 2bc' : 'Pnmm:2',
    'P 2ac 2ac -1ac' : 'Pmnm:1',
    '-P 2c 2a' : 'Pmnm:2',
    #  60
    '-P 2n 2ab' : 'Pbcn',
    '-P 2n 2c' : 'Pcan',
    '-P 2a 2n' : 'Pnca',
    '-P 2bc 2n' : 'Pnab',
    '-P 2ac 2b' : 'Pbna',
    '-P 2b 2ac' : 'Pcnb',
    #  61
    '-P 2ac 2ab' : 'Pbca',
    '-P 2bc 2ac' : 'Pcab',
    #  62
    '-P 2ac 2n' : 'Pnma',
    '-P 2bc 2a' : 'Pmnb',
    '-P 2c 2ab' : 'Pbnm',
    '-P 2n 2ac' : 'Pcmn',
    '-P 2n 2a' : 'Pmcn',
    '-P 2c 2n' : 'Pnam',
    #  63
    '-C 2c 2' : 'Cmcm',
    '-C 2c 2c' : 'Ccmm',
    '-A 2a 2a' : 'Amma',
    '-A 2 2a' : 'Amam',
    '-B 2 2b' : 'Bbmm',
    '-B 2b 2' : 'Bmmb',
    #  64
    '-C 2bc 2' : 'Cmca',
    '-C 2bc 2bc' : 'Ccmb',
    '-A 2ac 2ac' : 'Abma',
    '-A 2 2ac' : 'Acam',
    '-B 2 2bc' : 'Bbcm',
    '-B 2bc 2' : 'Bmab',
    #  65
    '-C 2 2' : 'Cmmm',
    '-A 2 2' : 'Ammm',
    '-B 2 2' : 'Bmmm',
    #  66
    '-C 2 2c' : 'Cccm',
    '-A 2a 2' : 'Amaa',
    '-B 2b 2b' : 'Bbmb',
    #  67
    '-C 2b 2' : 'Cmma',
    '-C 2b 2b' : 'Cmmb',
    '-A 2c 2c' : 'Abmm',
    '-A 2 2c' : 'Acmm',
    '-B 2 2c' : 'Bmcm',
    '-B 2c 2' : 'Bmam',
    #  68
    'C 2 2 -1bc' : 'Ccca:1',
    '-C 2b 2bc' : 'Ccca:2',
    'C 2 2 -1bc' : 'Cccb:1',
    '-C 2b 2c' : 'Cccb:2',
    'A 2 2 -1ac' : 'Abaa:1',
    '-A 2a 2c' : 'Abaa:2',
    'A 2 2 -1ac' : 'Acaa:1',
    '-A 2ac 2c' : 'Acaa:2',
    'B 2 2 -1bc' : 'Bbcb:1',
    '-B 2bc 2b' : 'Bbcb:2',
    'B 2 2 -1bc' : 'Bbab:1',
    '-B 2b 2bc' : 'Bbab:2',
    #  69
    '-F 2 2' : 'Fmmm',
    #  70
    'F 2 2 -1d' : 'Fddd:1',
    '-F 2uv 2vw' : 'Fddd:2',
    #  71
    '-I 2 2' : 'Immm',
    #  72
    '-I 2 2c' : 'Ibam',
    '-I 2a 2' : 'Imcb',
    '-I 2b 2b' : 'Icma',
    #  73
    '-I 2b 2c' : 'Ibca',
    '-I 2a 2b' : 'Icab',
    #  74
    '-I 2b 2' : 'Imma',
    '-I 2a 2a' : 'Immb',
    '-I 2c 2c' : 'Ibmm',
    '-I 2 2b' : 'Icmm',
    '-I 2 2a' : 'Imcm',
    '-I 2c 2' : 'Imam',
    #  75
    'P 4' : 'P4',
    #  76
    'P 4w' : 'P41',
    #  77
    'P 4c' : 'P42',
    #  78
    'P 4cw' : 'P43',
    #  79
    'I 4' : 'I4',
    #  80
    'I 4bw' : 'I41',
    #  81
    'P -4' : 'P-4',
    #  82
    'I -4' : 'I-4',
    #  83
    '-P 4' : 'P4/m',
    #  84
    '-P 4c' : 'P42/m',
    #  85
    'P 4ab -1ab' : 'P4/n:1',
    '-P 4a' : 'P4/n:2',
    #  86
    'P 4n -1n' : 'P42/n:1',
    '-P 4bc' : 'P42/n:2',
    #  87
    '-I 4' : 'I4/m',
    #  88
    'I 4bw -1bw' : 'I41/a:1',
    '-I 4ad' : 'I41/a:2',
    #  89
    'P 4 2' : 'P422',
    #  90
    'P 4ab 2ab' : 'P4212',
    #  91
    'P 4w 2c' : 'P4122',
    #  92
    'P 4abw 2nw' : 'P41212',
    #  93
    'P 4c 2' : 'P4222',
    #  94
    'P 4n 2n' : 'P42212',
    #  95
    'P 4cw 2c' : 'P4322',
    #  96
    'P 4nw 2abw' : 'P43212',
    #  97
    'I 4 2' : 'I422',
    #  98
    'I 4bw 2bw' : 'I4122',
    #  99
    'P 4 -2' : 'P4mm',
    # 100
    'P 4 -2ab' : 'P4bm',
    # 101
    'P 4c -2c' : 'P42cm',
    # 102
    'P 4n -2n' : 'P42nm',
    # 103
    'P 4 -2c' : 'P4cc',
    # 104
    'P 4 -2n' : 'P4nc',
    # 105
    'P 4c -2' : 'P42mc',
    # 106
    'P 4c -2ab' : 'P42bc',
    # 107
    'I 4 -2' : 'I4mm',
    # 108
    'I 4 -2c' : 'I4cm',
    # 109
    'I 4bw -2' : 'I41md',
    # 110
    'I 4bw -2c' : 'I41cd',
    # 111
    'P -4 2' : 'P-42m',
    # 112
    'P -4 2c' : 'P-42c',
    # 113
    'P -4 2ab' : 'P-421m',
    # 114
    'P -4 2n' : 'P-421c',
    # 115
    'P -4 -2' : 'P-4m2',
    # 116
    'P -4 -2c' : 'P-4c2',
    # 117
    'P -4 -2ab' : 'P-4b2',
    # 118
    'P -4 -2n' : 'P-4n2',
    # 119
    'I -4 -2' : 'I-4m2',
    # 120
    'I -4 -2c' : 'I-4c2',
    # 121
    'I -4 2' : 'I-42m',
    # 122
    'I -4 2bw' : 'I-42d',
    # 123
    '-P 4 2' : 'P4/mmm',
    # 124
    '-P 4 2c' : 'P4/mcc',
    # 125
    'P 4 2 -1ab' : 'P4/nbm:1',
    '-P 4a 2b' : 'P4/nbm:2',
    # 126
    'P 4 2 -1n' : 'P4/nnc:1',
    '-P 4a 2bc' : 'P4/nnc:2',
    # 127
    '-P 4 2ab' : 'P4/mbm',
    # 128
    '-P 4 2n' : 'P4/mnc',
    # 129
    'P 4ab 2ab -1ab' : 'P4/nmm:1',
    '-P 4a 2a' : 'P4/nmm:2',
    # 130
    'P 4ab 2n -1ab' : 'P4/ncc:1',
    '-P 4a 2ac' : 'P4/ncc:2',
    # 131
    '-P 4c 2' : 'P42/mmc',
    # 132
    '-P 4c 2c' : 'P42/mcm',
    # 133
    'P 4n 2c -1n' : 'P42/nbc:1',
    '-P 4ac 2b' : 'P42/nbc:2',
    # 134
    'P 4n 2 -1n' : 'P42/nnm:1',
    '-P 4ac 2bc' : 'P42/nnm:2',
    # 135
    '-P 4c 2ab' : 'P42/mbc',
    # 136
    '-P 4n 2n' : 'P42/mnm',
    # 137
    'P 4n 2n -1n' : 'P42/nmc:1',
    '-P 4ac 2a' : 'P42/nmc:2',
    # 138
    'P 4n 2ab -1n' : 'P42/ncm:1',
    '-P 4ac 2ac' : 'P42/ncm:2',
    # 139
    '-I 4 2' : 'I4/mmm',
    # 140
    '-I 4 2c' : 'I4/mcm',
    # 141
    'I 4bw 2bw -1bw' : 'I41/amd:1',
    '-I 4bd 2' : 'I41/amd:2',
    # 142
    'I 4bw 2aw -1bw' : 'I41/acd:1',
    '-I 4bd 2c' : 'I41/acd:2',
    # 143
    'P 3' : 'P3',
    # 144
    'P 31' : 'P31',
    # 145
    'P 32' : 'P32',
    # 146
    'R 3' : 'R3:H',
    'P 3*' : 'R3:R',
    # 147
    '-P 3' : 'P-3',
    # 148
    '-R 3' : 'R-3:H',
    '-P 3*' : 'R-3:R',
    # 149
    'P 3 2' : 'P312',
    # 150
    'P 3 2"' : 'P321',
    # 151
    'P 31 2c (0 0 1)' : 'P3112',
    # 152
    'P 31 2"' : 'P3121',
    # 153
    'P 32 2c (0 0 -1)' : 'P3212',
    # 154
    'P 32 2"' : 'P3221',
    # 155
    'R 3 2"' : 'R32:H',
    'P 3* 2' : 'R32:R',
    # 156
    'P 3 -2"' : 'P3m1',
    # 157
    'P 3 -2' : 'P31m',
    # 158
    'P 3 -2"c' : 'P3c1',
    # 159
    'P 3 -2c' : 'P31c',
    # 160
    'R 3 -2"' : 'R3m:H',
    'P 3* -2' : 'R3m:R',
    # 161
    'R 3 -2"c' : 'R3c:H',
    'P 3* -2n' : 'R3c:R',
    # 162
    '-P 3 2' : 'P-31m',
    # 163
    '-P 3 2c' : 'P-31c',
    # 164
    '-P 3 2"' : 'P-3m1',
    # 165
    '-P 3 2"c' : 'P-3c1',
    # 166
    '-R 3 2"' : 'R-3m:H',
    '-P 3* 2' : 'R-3m:R',
    # 167
    '-R 3 2"c' : 'R-3c:H',
    '-P 3* 2n' : 'R-3c:R',
    # 168
    'P 6' : 'P6',
    # 169
    'P 61' : 'P61',
    # 170
    'P 65' : 'P65',
    # 171
    'P 62' : 'P62',
    # 172
    'P 64' : 'P64',
    # 173
    'P 6c' : 'P63',
    # 174
    'P -6' : 'P-6',
    # 175
    '-P 6' : 'P6/m',
    # 176
    '-P 6c' : 'P63/m',
    # 177
    'P 6 2' : 'P622',
    # 178
    'P 61 2 (0 0 -1)' : 'P6122',
    # 179
    'P 65 2 (0 0 1)' : 'P6522',
    # 180
    'P 62 2c (0 0 1)' : 'P6222',
    # 181
    'P 64 2c (0 0 -1)' : 'P6422',
    # 182
    'P 6c 2c' : 'P6322',
    # 183
    'P 6 -2' : 'P6mm',
    # 184
    'P 6 -2c' : 'P6cc',
    # 185
    'P 6c -2' : 'P63cm',
    # 186
    'P 6c -2c' : 'P63mc',
    # 187
    'P -6 2' : 'P-6m2',
    # 188
    'P -6c 2' : 'P-6c2',
    # 189
    'P -6 -2' : 'P-62m',
    # 190
    'P -6c -2c' : 'P-62c',
    # 191
    '-P 6 2' : 'P6/mmm',
    # 192
    '-P 6 2c' : 'P6/mcc',
    # 193
    '-P 6c 2' : 'P63/mcm',
    # 194
    '-P 6c 2c' : 'P63/mmc',
    # 195
    'P 2 2 3' : 'P23',
    # 196
    'F 2 2 3' : 'F23',
    # 197
    'I 2 2 3' : 'I23',
    # 198
    'P 2ac 2ab 3' : 'P213',
    # 199
    'I 2b 2c 3' : 'I213',
    # 200
    '-P 2 2 3' : 'Pm-3',
    # 201
    'P 2 2 3 -1n' : 'Pn-3:1',
    '-P 2ab 2bc 3' : 'Pn-3:2',
    # 202
    '-F 2 2 3' : 'Fm-3',
    # 203
    'F 2 2 3 -1d' : 'Fd-3:1',
    '-F 2uv 2vw 3' : 'Fd-3:2',
    # 204
    '-I 2 2 3' : 'Im-3',
    # 205
    '-P 2ac 2ab 3' : 'Pa-3',
    # 206
    '-I 2b 2c 3' : 'Ia-3',
    # 207
    'P 4 2 3' : 'P432',
    # 208
    'P 4n 2 3' : 'P4232',
    # 209
    'F 4 2 3' : 'F432',
    # 210
    'F 4d 2 3' : 'F4132',
    # 211
    'I 4 2 3' : 'I432',
    # 212
    'P 4acd 2ab 3' : 'P4332',
    # 213
    'P 4bd 2ab 3' : 'P4132',
    # 214
    'I 4bd 2c 3' : 'I4132',
    # 215
    'P -4 2 3' : 'P-43m',
    # 216
    'F -4 2 3' : 'F-43m',
    # 217
    'I -4 2 3' : 'I-43m',
    # 218
    'P -4n 2 3' : 'P-43n',
    # 219
    'F -4c 2 3' : 'F-43c',
    # 220
    'I -4bd 2c 3' : 'I-43d',
    # 221
    '-P 4 2 3' : 'Pm-3m',
    # 222
    'P 4 2 3 -1n' : 'Pn-3n:1',
    '-P 4a 2bc 3' : 'Pn-3n:2',
    # 223
    '-P 4n 2 3' : 'Pm-3n',
    # 224
    'P 4n 2 3 -1n' : 'Pn-3m:1',
    '-P 4bc 2bc 3' : 'Pn-3m:2',
    # 225
    '-F 4 2 3' : 'Fm-3m',
    # 226
    '-F 4c 2 3' : 'Fm-3c',
    # 227
    'F 4d 2 3 -1d' : 'Fd-3m:1',
    '-F 4vw 2vw 3' : 'Fd-3m:2',
    # 228
    'F 4d 2 3 -1cd' : 'Fd-3c:1',
    '-F 4cvw 2vw 3' : 'Fd-3c:2',
    # 229
    '-I 4 2 3' : 'Im-3m',
    # 230
    '-I 4bd 2c 3' : 'Ia-3d',
    #######################
    # Non-standard settings
    # 1
    'A 1' : 'A1',
    'B 1' : 'B1',
    'C 1' : 'C1',
    'I 1' : 'I1',
    'F 1' : 'F1',
    # 2
    '-A 1' : 'A-1',
    '-B 1' : 'B-1',
    '-C 1' : 'C-1',
    '-I 1' : 'I-1',
    '-F 1' : 'F-1',
    # 5
    'F 2'  : 'F112',
    'F 2x' : 'F211',
    'F 2y' : 'F121',
    # 8
    'F -2' : 'F11m',
    'F -2x' : 'Fm11',
    'F -2y' : 'F1m1',
    # 9
    'F -2d'  : 'F11d',
    'F -2yd' : 'F1d1',
    'F -2xd' : 'Fd11',
    # 12
    '-F 2'  : 'F112/m',
    '-F 2x' : 'F2/m11',
    '-F 2y' : 'F12/m1',
    # 15
    'F 2ycuw -1c' : 'F12/d1',
    # 70
    '-F 2 2 -1d' : 'Fddd:1',
    '-F 2uv 2vw' : 'Fddd:2',
    # 139
    '-F 4 2' : 'F4/mmm'
}

Rhomb2HexHall = { 'P 3*'     : 'R 3',
                  '-P 3*'    : '-R 3',
                  'P 3* 2'   : 'R 3 2"',
                  'P 3* -2'  : 'R 3 -2"',
                  'P 3* -2n' : 'R 3 -2"c',
                  '-P 3* 2'  : '-R 3 2"',
                  '-P 3* 2n' : '-R 3 2"c'}

Hex2RhombHall = dict([])
for k,v in Rhomb2HexHall.items():
    Hex2RhombHall[v] = k

# A. Perlov's numbering -> international tables numbers
AP2Number = {
    1 : 1,
    2 : 2,
    3 : 3,
    4 : 3,
    5 : 4,
    6 : 4,
    7 : 5,
    8 : 5,
    9 : 5,
    10 : 5,
    11 : 5,
    12 : 5,
    13 : 6,
    14 : 6,
    15 : 7,
    16 : 7,
    17 : 7,
    18 : 7,
    19 : 7,
    20 : 7,
    21 : 8,
    22 : 8,
    23 : 8,
    24 : 8,
    25 : 8,
    26 : 8,
    27 : 9,
    28 : 9,
    29 : 9,
    30 : 9,
    31 : 9,
    32 : 9,
    33 : 9,
    34 : 9,
    35 : 9,
    36 : 9,
    37 : 9,
    38 : 9,
    39 : 10,
    40 : 10,
    41 : 11,
    42 : 11,
    43 : 12,
    44 : 12,
    45 : 12,
    46 : 12,
    47 : 12,
    48 : 12,
    49 : 13,
    50 : 13,
    51 : 13,
    52 : 13,
    53 : 13,
    54 : 13,
    55 : 14,
    56 : 14,
    57 : 14,
    58 : 14,
    59 : 14,
    60 : 14,
    61 : 15,
    62 : 15,
    63 : 15,
    64 : 15,
    65 : 15,
    66 : 15,
    67 : 15,
    68 : 15,
    69 : 15,
    70 : 15,
    71 : 15,
    72 : 15,
    73 : 16,
    74 : 17,
    75 : 17,
    76 : 17,
    77 : 18,
    78 : 18,
    79 : 18,
    80 : 19,
    81 : 20,
    82 : 20,
    83 : 20,
    84 : 21,
    85 : 21,
    86 : 21,
    87 : 22,
    88 : 23,
    89 : 24,
    90 : 25,
    91 : 25,
    92 : 25,
    93 : 26,
    94 : 26,
    95 : 26,
    96 : 26,
    97 : 26,
    98 : 26,
    99 : 27,
    100 : 27,
    101 : 27,
    102 : 28,
    103 : 28,
    104 : 28,
    105 : 28,
    106 : 28,
    107 : 28,
    108 : 29,
    109 : 29,
    110 : 29,
    111 : 29,
    112 : 29,
    113 : 29,
    114 : 30,
    115 : 30,
    116 : 30,
    117 : 30,
    118 : 30,
    119 : 30,
    120 : 31,
    121 : 31,
    122 : 31,
    123 : 31,
    124 : 31,
    125 : 31,
    126 : 32,
    127 : 32,
    128 : 32,
    129 : 33,
    130 : 33,
    131 : 33,
    132 : 33,
    133 : 33,
    134 : 33,
    135 : 34,
    136 : 34,
    137 : 34,
    138 : 35,
    139 : 35,
    140 : 35,
    145 : 36,
    146 : 36,
    143 : 36,
    144 : 36,
    141 : 36,
    142 : 36,
    147 : 37,
    148 : 37,
    149 : 37,
    150 : 38,
    151 : 38,
    152 : 38,
    153 : 38,
    154 : 38,
    155 : 38,
    156 : 39,
    157 : 39,
    158 : 39,
    159 : 39,
    160 : 39,
    161 : 39,
    162 : 40,
    163 : 40,
    164 : 40,
    165 : 40,
    166 : 40,
    167 : 40,
    168 : 41,
    169 : 41,
    170 : 41,
    171 : 41,
    172 : 41,
    173 : 41,
    174 : 42,
    175 : 42,
    176 : 42,
    177 : 43,
    178 : 43,
    179 : 43,
    180 : 44,
    181 : 44,
    182 : 44,
    183 : 45,
    184 : 45,
    185 : 45,
    186 : 46,
    187 : 46,
    188 : 46,
    189 : 46,
    190 : 46,
    191 : 46,
    192 : 47,
    193 : 48,
    194 : 48,
    195 : 49,
    196 : 49,
    197 : 49,
    198 : 50,
    199 : 50,
    200 : 50,
    201 : 50,
    202 : 50,
    203 : 50,
    204 : 51,
    205 : 51,
    206 : 51,
    207 : 51,
    208 : 51,
    209 : 51,
    210 : 52,
    211 : 52,
    212 : 52,
    213 : 52,
    214 : 52,
    215 : 52,
    216 : 53,
    217 : 53,
    218 : 53,
    219 : 53,
    220 : 53,
    221 : 53,
    222 : 54,
    223 : 54,
    224 : 54,
    225 : 54,
    226 : 54,
    227 : 54,
    228 : 55,
    229 : 55,
    230 : 55,
    231 : 56,
    232 : 56,
    233 : 56,
    234 : 57,
    235 : 57,
    236 : 57,
    237 : 57,
    238 : 57,
    239 : 57,
    240 : 58,
    241 : 58,
    242 : 58,
    247 : 59,
    248 : 59,
    245 : 59,
    246 : 59,
    243 : 59,
    244 : 59,
    249 : 60,
    250 : 60,
    251 : 60,
    252 : 60,
    253 : 60,
    254 : 60,
    255 : 61,
    256 : 61,
    257 : 62,
    258 : 62,
    259 : 62,
    260 : 62,
    261 : 62,
    262 : 62,
    263 : 63,
    264 : 63,
    265 : 63,
    266 : 63,
    267 : 63,
    268 : 63,
    269 : 64,
    270 : 64,
    271 : 64,
    272 : 64,
    273 : 64,
    274 : 64,
    275 : 65,
    276 : 65,
    277 : 65,
    278 : 66,
    279 : 66,
    280 : 66,
    281 : 67,
    282 : 67,
    283 : 67,
    284 : 67,
    285 : 67,
    286 : 67,
    287 : 68,
    288 : 68,
    289 : 68,
    290 : 68,
    291 : 68,
    292 : 68,
    293 : 68,
    294 : 68,
    295 : 68,
    296 : 68,
    297 : 68,
    298 : 68,
    299 : 69,
    300 : 70,
    301 : 70,
    302 : 71,
    303 : 72,
    304 : 72,
    305 : 72,
    306 : 73,
    307 : 73,
    308 : 74,
    309 : 74,
    310 : 74,
    311 : 74,
    312 : 74,
    313 : 74,
    314 : 75,
    315 : 76,
    316 : 77,
    317 : 78,
    318 : 79,
    319 : 80,
    320 : 81,
    321 : 82,
    322 : 83,
    323 : 84,
    324 : 85,
    325 : 85,
    326 : 86,
    327 : 86,
    328 : 87,
    329 : 88,
    330 : 88,
    331 : 89,
    332 : 90,
    333 : 91,
    334 : 92,
    335 : 93,
    336 : 94,
    337 : 95,
    338 : 96,
    339 : 97,
    340 : 98,
    341 : 99,
    342 : 100,
    343 : 101,
    344 : 102,
    345 : 103,
    346 : 104,
    347 : 105,
    348 : 106,
    349 : 107,
    350 : 108,
    351 : 109,
    352 : 110,
    353 : 111,
    354 : 112,
    355 : 113,
    356 : 114,
    357 : 115,
    358 : 116,
    359 : 117,
    360 : 118,
    361 : 119,
    362 : 120,
    363 : 121,
    364 : 122,
    365 : 123,
    366 : 124,
    367 : 125,
    368 : 125,
    369 : 126,
    370 : 126,
    371 : 127,
    372 : 128,
    373 : 129,
    374 : 129,
    375 : 130,
    376 : 130,
    377 : 131,
    378 : 132,
    379 : 133,
    380 : 133,
    381 : 134,
    382 : 134,
    383 : 135,
    384 : 136,
    385 : 137,
    386 : 137,
    387 : 138,
    388 : 138,
    389 : 139,
    390 : 140,
    391 : 141,
    392 : 141,
    393 : 142,
    394 : 142,
    395 : 143,
    396 : 143,
    397 : 144,
    398 : 144,
    399 : 145,
    400 : 145,
    402 : 146,
    401 : 146,
    403 : 147,
    404 : 147,
    406 : 148,
    405 : 148,
    407 : 149,
    408 : 150,
    409 : 151,
    410 : 152,
    411 : 153,
    412 : 154,
    414 : 155,
    413 : 155,
    415 : 156,
    416 : 157,
    417 : 158,
    418 : 159,
    420 : 160,
    419 : 160,
    422 : 161,
    421 : 161,
    423 : 162,
    424 : 163,
    425 : 164,
    426 : 165,
    428 : 166,
    427 : 166,
    430 : 167,
    429 : 167,
    431 : 168,
    432 : 169,
    433 : 170,
    434 : 171,
    435 : 172,
    436 : 173,
    437 : 174,
    438 : 175,
    439 : 176,
    440 : 177,
    441 : 178,
    442 : 179,
    443 : 180,
    444 : 181,
    445 : 182,
    446 : 183,
    447 : 184,
    448 : 185,
    449 : 186,
    450 : 187,
    451 : 188,
    452 : 189,
    453 : 190,
    454 : 191,
    455 : 192,
    456 : 193,
    457 : 194,
    458 : 195,
    459 : 196,
    460 : 197,
    461 : 198,
    462 : 199,
    463 : 200,
    464 : 201,
    465 : 201,
    466 : 202,
    467 : 203,
    468 : 203,
    469 : 204,
    470 : 205,
    471 : 206,
    472 : 207,
    473 : 208,
    474 : 209,
    475 : 210,
    476 : 211,
    477 : 212,
    478 : 213,
    479 : 214,
    480 : 215,
    481 : 216,
    482 : 217,
    483 : 218,
    484 : 219,
    485 : 220,
    486 : 221,
    487 : 222,
    488 : 222,
    489 : 223,
    490 : 224,
    491 : 224,
    492 : 225,
    493 : 226,
    494 : 227,
    495 : 227,
    496 : 228,
    497 : 228,
    498 : 229,
    499 : 230,
    500 : 14,
    501 : 14,
    502 : 14
    }

# international tables numbers -> A. Perlovs numbering
Number2AP = {
    1 : 1,
    2 : 2,
    3 : 3,
    4 : 5,
    5 : 7,
    6 :  13,
    7 :  15,
    8 :  21,
    9 :  27,
    10 : 39,
    11 : 41,
    12 : 43,
    13 : 50,
    14 : 55,
    15 : 61,
    16 : 73,
    17 : 74,
    18 : 77,
    19 : 80,
    20 : 81,
    21 : 84,
    22 : 87,
    23 : 88,
    24 : 89,
    25 : 90,
    26 : 93,
    27 : 99,
    28 : 102,
    29 : 108,
    30 : 114,
    31 : 120,
    32 : 126,
    33 : 129,
    34 : 135,
    35 : 138,
    36 : 145,
    37 : 147,
    38 : 150,
    39 : 156,
    40 : 162,
    41 : 168,
    42 : 174,
    43 : 177,
    44 : 180,
    45 : 183,
    46 : 186,
    47 : 192,
    48 : 193,
    49 : 195,
    50 : 198,
    51 : 204,
    52 : 210,
    53 : 216,
    54 : 222,
    55 : 228,
    56 : 231,
    57 : 234,
    58 : 240,
    59 : 247,
    60 : 249,
    61 : 255,
    62 : 257,
    63 : 263,
    64 : 269,
    65 : 275,
    66 : 278,
    67 : 281,
    68 : 287,
    69 : 299,
    70 : 300,
    71 : 302,
    72 : 303,
    73 : 306,
    74 : 308,
    75 : 314,
    76 : 315,
    77 : 316,
    78 : 317,
    79 : 318,
    80 : 319,
    81 : 320,
    82 : 321,
    83 : 322,
    84 : 323,
    85 : 324,
    86 : 326,
    87 : 328,
    88 : 329,
    89 : 331,
    90 : 332,
    91 : 333,
    92 : 334,
    93 : 335,
    94 : 336,
    95 : 337,
    96 : 338,
    97 : 339,
    98 : 340,
    99 : 341,
    100 : 342,
    101 : 343,
    102 : 344,
    103 : 345,
    104 : 346,
    105 : 347,
    106 : 348,
    107 : 349,
    108 : 350,
    109 : 351,
    110 : 352,
    111 : 353,
    112 : 354,
    113 : 355,
    114 : 356,
    115 : 357,
    116 : 358,
    117 : 359,
    118 : 360,
    119 : 361,
    120 : 362,
    121 : 363,
    122 : 364,
    123 : 365,
    124 : 366,
    125 : 368,
    126 : 370,
    127 : 371,
    128 : 372,
    129 : 374,
    130 : 376,
    131 : 377,
    132 : 378,
    133 : 380,
    134 : 382,
    135 : 383,
    136 : 384,
    137 : 386,
    138 : 388,
    139 : 389,
    140 : 390,
    141 : 392,
    142 : 394,
    143 : 396,
    144 : 398,
    145 : 400,
    146 : 401,
    147 : 404,
    148 : 405,
    149 : 407,
    150 : 408,
    151 : 409,
    152 : 410,
    153 : 411,
    154 : 412,
    155 : 414,
    156 : 415,
    157 : 416,
    158 : 417,
    159 : 418,
    160 : 420,
    160 : 419,
    161 : 422,
    162 : 423,
    163 : 424,
    164 : 425,
    165 : 426,
    166 : 428,
    167 : 430,
    168 : 431,
    169 : 432,
    170 : 433,
    171 : 434,
    172 : 435,
    173 : 436,
    174 : 437,
    175 : 438,
    176 : 439,
    177 : 440,
    178 : 441,
    179 : 442,
    180 : 443,
    181 : 444,
    182 : 445,
    183 : 446,
    184 : 447,
    185 : 448,
    186 : 449,
    187 : 450,
    188 : 451,
    189 : 452,
    190 : 453,
    191 : 454,
    192 : 455,
    193 : 456,
    194 : 457,
    195 : 458,
    196 : 459,
    197 : 460,
    198 : 461,
    199 : 462,
    200 : 463,
    201 : 465,
    202 : 466,
    203 : 468,
    204 : 469,
    205 : 470,
    206 : 471,
    207 : 472,
    208 : 473,
    209 : 474,
    210 : 475,
    211 : 476,
    212 : 477,
    213 : 478,
    214 : 479,
    215 : 480,
    216 : 481,
    217 : 482,
    218 : 483,
    219 : 484,
    220 : 485,
    221 : 486,
    222 : 488,
    223 : 489,
    224 : 491,
    225 : 492,
    226 : 493,
    227 : 494,
    229 : 498,
230 : 499
    }

# Symmetry operations in XYZ form from Hall symbol
SymOpsHall = {
    'P 1' : [['x',' y',' z']],
    '-P 1' : [['x',' y',' z'],
              ['-x',' -y',' -z']],
    'P 2y' : [['x',' y',' z'],
              ['-x',' y',' -z']],
    'P 2' : [['x',' y',' z'],
              ['-x',' -y',' z']],
    'P 2x' : [['x',' y',' z'],
              ['x',' -y',' -z']],
    'P 2yb' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z']],
    'P 2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2']],
    'P 2xa' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z']],
    'C 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z']],
    'A 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2']],
    'I 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2']],
    'A 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2']],
    'B 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2']],
    'I 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2']],
    'B 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2']],
    'C 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z']],
    'I 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2']],
    'P -2y' : [['x',' y',' z'],
              ['x',' -y',' z']],
    'P -2' : [['x',' y',' z'],
              ['x',' y',' -z']],
    'P -2x' : [['x',' y',' z'],
              ['-x',' y',' z']],
    'P -2yc' : [['x',' y',' z'],
              ['x',' -y',' z+1/2']],
    'P -2yac' : [['x',' y',' z'],
              ['x+1/2',' -y',' z+1/2']],
    'P -2ya' : [['x',' y',' z'],
              ['x+1/2',' -y',' z']],
    'P -2a' : [['x',' y',' z'],
              ['x+1/2',' y',' -z']],
    'P -2ab' : [['x',' y',' z'],
              ['x+1/2',' y+1/2',' -z']],
    'P -2b' : [['x',' y',' z'],
              ['x',' y+1/2',' -z']],
    'P -2xb' : [['x',' y',' z'],
              ['-x',' y+1/2',' z']],
    'P -2xbc' : [['x',' y',' z'],
              ['-x',' y+1/2',' z+1/2']],
    'P -2xc' : [['x',' y',' z'],
              ['-x',' y',' z+1/2']],
    # 8
    'C -2y' : [['x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'A -2y' : [['x',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'I -2y' : [['x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'A -2' : [['x',' y',' z'],
              ['x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['x',' y+1/2',' -z+1/2']],
    'B -2' : [['x',' y',' z'],
              ['x',' y',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' y',' -z+1/2']],
    'I -2' : [['x',' y',' z'],
              ['x',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    'B -2x' : [['x',' y',' z'],
              ['-x',' y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'C -2x' : [['x',' y',' z'],
              ['-x',' y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' z']],
    'I -2x' : [['x',' y',' z'],
              ['-x',' y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    # 9
    'C -2yc' : [['x',' y',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'A -2yac' : [['x',' y',' z'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    'I -2ya' : [['x',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'A -2ya' : [['x',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'C -2ybc' : [['x',' y',' z'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' z+1/2']],
    'I -2yc' : [['x',' y',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    'A -2a' : [['x',' y',' z'],
              ['x+1/2',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    'B -2bc' : [['x',' y',' z'],
              ['x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' -z']],
    'I -2b' : [['x',' y',' z'],
              ['x',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' y',' -z+1/2']],
    'B -2b' : [['x',' y',' z'],
              ['x',' y+1/2',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    'A -2ac' : [['x',' y',' z'],
              ['x+1/2',' y',' -z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' -z']],
    'I -2a' : [['x',' y',' z'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x',' y+1/2',' -z+1/2']],
    'B -2xb' : [['x',' y',' z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'C -2xbc' : [['x',' y',' z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y',' z+1/2']],
    'I -2xc' : [['x',' y',' z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z']],
    'C -2xc' : [['x',' y',' z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'B -2xbc' : [['x',' y',' z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y+1/2',' z']],
    'I -2xb' : [['x',' y',' z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    '-P 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z']],
    '-P 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z']],
    '-P 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z']],
    '-P 2yb' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' -y+1/2',' z']],
    '-P 2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2']],
    '-P 2xa' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' -y',' -z'],
              ['-x+1/2',' y',' z']],
    '-C 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-I 2y' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-A 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2']],
    '-B 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2']],
    '-I 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    '-B 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    '-C 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    '-I 2x' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    '-P 2yc' : [['x',' y',' z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z+1/2']],
    '-P 2yac' : [['x',' y',' z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2ya' : [['x',' y',' z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y',' z']],
    '-P 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z']],
    '-P 2ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z']],
    '-P 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z']],
    '-P 2xb' : [['x',' y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y+1/2',' z']],
    '-P 2xbc' : [['x',' y',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x',' y+1/2',' z+1/2']],
    '-P 2xc' : [['x',' y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z+1/2']],
    '-P 2ybc' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2yn' : [['x',' y',' z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2yab' : [['x',' y',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2']],
    '-P 2n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    '-P 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2']],
    '-P 2xab' : [['x',' y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    '-P 2xn' : [['x',' y',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    '-P 2xac' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x+1/2',' y',' z+1/2']],
    '-C 2yc' : [['x',' y',' z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-A 2yac' : [['x',' y',' z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-I 2ya' : [['x',' y',' z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-A 2ya' : [['x',' y',' z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-C 2ybc' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' -y',' z+1/2']],
    '-I 2yc' : [['x',' y',' z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    '-B 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z']],
    '-I 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2']],
    '-B 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    '-A 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z']],
    '-I 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2']],
    '-B 2xb' : [['x',' y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    '-C 2xbc' : [['x',' y',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y',' z+1/2']],
    '-I 2xc' : [['x',' y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z']],
    '-C 2xc' : [['x',' y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    '-B 2xbc' : [['x',' y',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z']],
    '-I 2xb' : [['x',' y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'P 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z']],
    'P 2c 2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z+1/2']],
    'P 2a 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y',' -z']],
    'P 2 2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z']],
    'P 2 2ab' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z']],
    'P 2bc 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z+1/2']],
    'P 2ac 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y',' -z']],
    'P 2ac 2ab' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2']],
    'C 2c 2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2']],
    'A 2a 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2']],
    'B 2 2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2']],
    'C 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z']],
    'A 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2']],
    'B 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2']],
    'F 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z']],
    'I 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2']],
    'I 2b 2c' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2']],
    'P 2 -2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z']],
    'P -2 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' -y',' z']],
    'P -2 -2' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z']],
    'P 2c -2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z+1/2']],
    'P 2c -2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z']],
    'P -2a 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x',' -y',' z']],
    'P -2 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x',' y',' -z'],
              ['x+1/2',' -y',' z']],
    'P -2 -2b' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z']],
    'P -2b -2' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z']],
    'P 2 -2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2']],
    'P -2a 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' -y',' z']],
    'P -2b -2b' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z']],
    'P 2 -2a' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z']],
    'P 2 -2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z']],
    'P -2b 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x',' -y+1/2',' z']],
    'P -2c 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x',' -y',' z+1/2']],
    'P -2c -2c' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2']],
    'P -2a -2a' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z']],
    'P 2c -2ac' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z']],
    'P 2c -2b' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    'P -2b 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    'P -2ac 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['x',' -y',' z+1/2']],
    'P -2bc -2c' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y',' z+1/2']],
    'P -2a -2ab' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    'P 2 -2bc' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'P 2 -2ac' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'P -2ac 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'P -2ab 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    'P -2ab -2ab' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    'P -2bc -2bc' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2']],
    'P 2ac -2' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x',' y',' z'],
              ['x+1/2',' -y',' z+1/2']],
    'P 2bc -2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z']],
    'P -2ab 2ab' : [['x',' y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['x',' -y',' z']],
    'P -2 2ac' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x',' y',' -z'],
              ['x+1/2',' -y',' z+1/2']],
    'P -2 -2bc' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z+1/2']],
    'P -2ab -2' : [['x',' y',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y',' z']],
    'P 2 -2ab' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'P -2bc 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'P -2ac -2ac' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'P 2c -2n' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    'P 2c -2ab' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'P -2bc 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'P -2n 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'P -2n -2ac' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'P -2ac -2n' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'P 2 -2n' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'P -2n 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'P -2n -2n' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'C 2 -2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'A -2 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'B -2 -2' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'C 2c -2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'C 2c -2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    'A -2a 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'A -2 2a' : [['x',' y',' z'],
              ['x+1/2',' -y',' -z'],
              ['x',' y',' -z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'B -2 -2b' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'B -2b -2' : [['x',' y',' z'],
              ['-x',' y+1/2',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'C 2 -2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'A -2a 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'B -2b -2b' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'A 2 -2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'B 2 -2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'B -2 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' -y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'C -2 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    'C -2 -2' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    'A -2 -2' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2']],
    'A 2 -2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z']],
    'B 2 -2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z']],
    'B -2c 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' -y',' z']],
    'C -2b 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' -y',' z']],
    'C -2b -2b' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z']],
    'A -2c -2c' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z']],
    'A 2 -2a' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'B 2 -2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'B -2b 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'C -2c 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'C -2c -2c' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'A -2a -2a' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'A 2 -2ac' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'B 2 -2bc' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'B -2bc 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    'C -2bc 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'C -2bc -2bc' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'A -2ac -2ac' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    'F 2 -2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'F -2 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    'F -2 -2' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    'F 2 -2d' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/4',' y+1/4',' z+1/4'],
              ['x+1/4',' -y+1/4',' z+1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-x+1/4',' y-1/4',' z-1/4'],
              ['x+1/4',' -y-1/4',' z-1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-x-1/4',' y+1/4',' z-1/4'],
              ['x-1/4',' -y+1/4',' z-1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-x-1/4',' y-1/4',' z+1/4'],
              ['x-1/4',' -y-1/4',' z+1/4']],
    'F -2d 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/4',' y+1/4',' -z+1/4'],
              ['x+1/4',' -y+1/4',' z+1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x+1/4',' y-1/4',' -z-1/4'],
              ['x+1/4',' -y-1/4',' z-1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x-1/4',' y+1/4',' -z-1/4'],
              ['x-1/4',' -y+1/4',' z-1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x-1/4',' y-1/4',' -z+1/4'],
              ['x-1/4',' -y-1/4',' z+1/4']],
    'F -2d -2d' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/4',' y+1/4',' -z+1/4'],
              ['-x+1/4',' y+1/4',' z+1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/4',' y-1/4',' -z-1/4'],
              ['-x+1/4',' y-1/4',' z-1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x-1/4',' y+1/4',' -z-1/4'],
              ['-x-1/4',' y+1/4',' z-1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x-1/4',' y-1/4',' -z+1/4'],
              ['-x-1/4',' y-1/4',' z+1/4']],
    'I 2 -2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'I -2 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'I -2 -2' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2']],
    'I 2 -2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'I -2a 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'I -2b -2b' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2']],
    'I 2 -2a' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    'I 2 -2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'I -2b 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'I -2c 2' : [['x',' y',' z'],
              ['x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['x+1/2',' -y+1/2',' z']],
    'I -2c -2c' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z']],
    'I -2a -2a' : [['x',' y',' z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2']],
    '-P 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z']],
    'P 2 2 -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2ab 2bc' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2 2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2']],
    '-P 2a 2' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' -y',' z']],
    '-P 2b 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z']],
    'P 2 2 -1ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2ab 2b' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y',' z']],
    'P 2 2 -1bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2b 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z+1/2']],
    'P 2 2 -1ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2a 2c' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2a 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x',' -y',' z']],
    '-P 2b 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z']],
    '-P 2 2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z']],
    '-P 2c 2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z']],
    '-P 2c 2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z+1/2']],
    '-P 2 2a' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z']],
    '-P 2a 2bc' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2b 2n' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2n 2b' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2ab 2c' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2ab 2n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y',' z+1/2']],
    '-P 2n 2bc' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z']],
    '-P 2ac 2' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x',' y',' z'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2bc 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z']],
    '-P 2ab 2ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y',' z']],
    '-P 2 2ac' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2 2bc' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2ab 2' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x',' -y',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2a 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y',' z+1/2']],
    '-P 2b 2c' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2a 2b' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2ac 2c' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z']],
    '-P 2bc 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z+1/2']],
    '-P 2b 2ab' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' z']],
    '-P 2 2ab' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2bc 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2ac 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y',' z']],
    '-P 2ab 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2ac 2bc' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2bc 2ab' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2c 2b' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2c 2ac' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z']],
    '-P 2ac 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x',' -y',' z+1/2']],
    '-P 2b 2a' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2a 2ab' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z']],
    '-P 2bc 2c' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y+1/2',' z']],
    '-P 2 2n' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2n 2' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2n 2n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y',' z']],
    'P 2 2ab -1ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z']],
    '-P 2ab 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y',' z'],
              ['x',' -y+1/2',' z']],
    'P 2bc 2 -1bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z']],
    '-P 2c 2bc' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z']],
    'P 2ac 2ac -1ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2c 2a' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z+1/2']],
    '-P 2n 2ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y',' z+1/2']],
    '-P 2n 2c' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2a 2n' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2bc 2n' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z']],
    '-P 2ac 2b' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2b 2ac' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2ac 2ab' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2bc 2ac' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-P 2ac 2n' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z']],
    '-P 2bc 2a' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2c 2ab' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2n 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y+1/2',' z']],
    '-P 2n 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-P 2c 2n' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-C 2c 2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-C 2c 2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2a 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-A 2 2a' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-B 2 2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-B 2b 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-C 2bc 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' z+1/2']],
    '-C 2bc 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2ac 2ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-A 2 2ac' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-B 2 2bc' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-B 2bc 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-C 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-B 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-C 2 2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-A 2a 2' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-B 2b 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-C 2b 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' z']],
    '-C 2b 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2c 2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-A 2 2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z']],
    '-B 2 2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z']],
    '-B 2c 2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z']],
    'C 2 2 -1bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-C 2b 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'C 2 2 -1bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-C 2b 2c' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    'A 2 2 -1ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2a 2c' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'A 2 2 -1ac' : [['x',' y',' z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-A 2ac 2c' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'B 2 2 -1bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-B 2bc 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z']],
    'B 2 2 -1bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-B 2b 2bc' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y',' z']],
    '-F 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'F 2 2 -1d' : [['x',' y',' z'],
              ['-x+1/4',' -y+1/4',' -z+1/4'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/4',' y+1/4',' -z+1/4'],
              ['-x+1/4',' y+1/4',' z+1/4'],
              ['x+1/4',' -y+1/4',' z+1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/4',' -y-1/4',' -z-1/4'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/4',' y-1/4',' -z-1/4'],
              ['-x+1/4',' y-1/4',' z-1/4'],
              ['x+1/4',' -y-1/4',' z-1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['-x-1/4',' -y+1/4',' -z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x-1/4',' y+1/4',' -z-1/4'],
              ['-x-1/4',' y+1/4',' z-1/4'],
              ['x-1/4',' -y+1/4',' z-1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['-x-1/4',' -y-1/4',' -z+1/4'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x-1/4',' y-1/4',' -z+1/4'],
              ['-x-1/4',' y-1/4',' z+1/4'],
              ['x-1/4',' -y-1/4',' z+1/4']],
    '-F 2uv 2vw' : [['x',' y',' z'],
              ['-x+1/4',' -y+1/4',' z'],
              ['x',' -y+1/4',' -z+1/4'],
              ['-x+1/4',' y',' -z+1/4'],
              ['-x',' -y',' -z'],
              ['x-1/4',' y-1/4',' -z'],
              ['-x',' y-1/4',' z-1/4'],
              ['x-1/4',' -y',' z-1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/4',' -y-1/4',' z+1/2'],
              ['x',' -y-1/4',' -z-1/4'],
              ['-x+1/4',' y+1/2',' -z-1/4'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['x-1/4',' y+1/4',' -z+1/2'],
              ['-x',' y+1/4',' z+1/4'],
              ['x-1/4',' -y+1/2',' z+1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['-x-1/4',' -y+1/4',' z+1/2'],
              ['x+1/2',' -y+1/4',' -z-1/4'],
              ['-x-1/4',' y',' -z-1/4'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['x+1/4',' y-1/4',' -z+1/2'],
              ['-x+1/2',' y-1/4',' z+1/4'],
              ['x+1/4',' -y',' z+1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['-x-1/4',' -y-1/4',' z'],
              ['x+1/2',' -y-1/4',' -z+1/4'],
              ['-x-1/4',' y+1/2',' -z+1/4'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['x+1/4',' y+1/4',' -z'],
              ['-x+1/2',' y+1/4',' z-1/4'],
              ['x+1/4',' -y+1/2',' z-1/4']],
    '-I 2 2' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-I 2 2c' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    '-I 2a 2' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-I 2b 2b' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-I 2b 2c' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-I 2a 2b' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    '-I 2b 2' : [['x',' y',' z'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-I 2a 2a' : [['x',' y',' z'],
              ['-x+1/2',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x+1/2',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-I 2c 2c' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-I 2 2b' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x',' y+1/2',' z'],
              ['x',' -y+1/2',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-I 2 2a' : [['x',' y',' z'],
              ['-x',' -y',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z'],
              ['-x+1/2',' y',' z'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2']],
    '-I 2c 2' : [['x',' y',' z'],
              ['-x',' -y',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['x',' y',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z']],
    'P 4' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z']],
    'P 4w' : [['x',' y',' z'],
              ['-y',' x',' z+1/4'],
              ['-x',' -y',' z+1/2'],
              ['y',' -x',' z-1/4']],
    'P 4c' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2']],
    'P 4cw' : [['x',' y',' z'],
              ['-y',' x',' z-1/4'],
              ['-x',' -y',' z+1/2'],
              ['y',' -x',' z+1/4']],
    'I 4' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2']],
    'I 4bw' : [['x',' y',' z'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4']],
    'P -4' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z']],
    'I -4' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2']],
    '-P 4' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z']],
    '-P 4c' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y',' x',' -z+1/2']],
    'P 4ab -1ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-y+1/2',' x+1/2',' z'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' y+1/2',' -z']],
    '-P 4a' : [['x',' y',' z'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z']],
    'P 4n -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2']],
    '-P 4bc' : [['x',' y',' z'],
              ['-y',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y+1/2',' -x',' z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y+1/2',' x',' -z+1/2']],
    '-I 4' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2']],
    'I 4bw -1bw' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/4'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x',' y+1/2',' -z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' -z-1/4'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z-1/4']],
    '-I 4ad' : [['x',' y',' z'],
              ['-y-1/4',' x+1/4',' z+1/4'],
              ['-x',' -y+1/2',' z'],
              ['y+1/4',' -x+1/4',' z+1/4'],
              ['-x',' -y',' -z'],
              ['y+1/4',' -x-1/4',' -z-1/4'],
              ['x',' y+1/2',' -z'],
              ['-y-1/4',' x-1/4',' -z-1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/4',' x-1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x-1/4',' z-1/4'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y-1/4',' -x+1/4',' -z+1/4'],
              ['x+1/2',' y',' -z+1/2'],
              ['-y+1/4',' x+1/4',' -z+1/4']],
    'P 4 2' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z']],
    'P 4ab 2ab' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z']],
    'P 4w 2c' : [['x',' y',' z'],
              ['-y',' x',' z+1/4'],
              ['-x',' -y',' z+1/2'],
              ['y',' -x',' z-1/4'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['y',' x',' -z-1/4'],
              ['-y',' -x',' -z+1/4']],
    'P 4abw 2nw' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z+1/4'],
              ['-x',' -y',' z+1/2'],
              ['y+1/2',' -x+1/2',' z-1/4'],
              ['x+1/2',' -y+1/2',' -z-1/4'],
              ['-x+1/2',' y+1/2',' -z+1/4'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z+1/2']],
    'P 4c 2' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2']],
    'P 4n 2n' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z']],
    'P 4cw 2c' : [['x',' y',' z'],
              ['-y',' x',' z-1/4'],
              ['-x',' -y',' z+1/2'],
              ['y',' -x',' z+1/4'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z'],
              ['y',' x',' -z+1/4'],
              ['-y',' -x',' -z-1/4']],
    'P 4nw 2abw' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z-1/4'],
              ['-x',' -y',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/4'],
              ['x+1/2',' -y+1/2',' -z+1/4'],
              ['-x+1/2',' y+1/2',' -z-1/4'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z+1/2']],
    'I 4 2' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2']],
    'I 4bw 2bw' : [['x',' y',' z'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['x',' -y+1/2',' -z+1/4'],
              ['-x',' y+1/2',' -z+1/4'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4'],
              ['x+1/2',' -y',' -z-1/4'],
              ['-x+1/2',' y',' -z-1/4'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2']],
    'P 4 -2' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    'P 4 -2ab' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    'P 4c -2c' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    'P 4n -2n' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    'P 4 -2c' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2']],
    'P 4 -2n' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'P 4c -2' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2']],
    'P 4c -2ab' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'I 4 -2' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'I 4 -2c' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    'I 4bw -2' : [['x',' y',' z'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x+1/2',' z+1/4'],
              ['y',' x+1/2',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x',' z-1/4'],
              ['y+1/2',' x',' z-1/4']],
    'I 4bw -2c' : [['x',' y',' z'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y+1/2',' -x',' z+1/4'],
              ['y+1/2',' x',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y',' -x+1/2',' z-1/4'],
              ['y',' x+1/2',' z-1/4']],
    'P -4 2' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    'P -4 2c' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2']],
    'P -4 2ab' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    'P -4 2n' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'P -4 -2' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z']],
    'P -4 -2c' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2']],
    'P -4 -2ab' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'P -4 -2n' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'I -4 -2' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    'I -4 -2c' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'I -4 2' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'I -4 2bw' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['x',' -y+1/2',' -z+1/4'],
              ['-x',' y+1/2',' -z+1/4'],
              ['-y',' -x+1/2',' z+1/4'],
              ['y',' x+1/2',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['x+1/2',' -y',' -z-1/4'],
              ['-x+1/2',' y',' -z-1/4'],
              ['-y+1/2',' -x',' z-1/4'],
              ['y+1/2',' x',' z-1/4']],
    '-P 4 2' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    '-P 4 2c' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2']],
    'P 4 2 -1ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['y+1/2',' -x+1/2',' -z'],
              ['-y+1/2',' x+1/2',' -z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    '-P 4a 2b' : [['x',' y',' z'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z'],
              ['y',' x',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y',' z'],
              ['-y',' -x',' z'],
              ['y+1/2',' x+1/2',' z']],
    'P 4 2 -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    '-P 4a 2bc' : [['x',' y',' z'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    '-P 4 2ab' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    '-P 4 2n' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'P 4ab 2ab -1ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-y+1/2',' x+1/2',' z'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    '-P 4a 2a' : [['x',' y',' z'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z'],
              ['-x+1/2',' y',' z'],
              ['x',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y',' x',' z']],
    'P 4ab 2n -1ab' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-y+1/2',' x+1/2',' z'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    '-P 4a 2ac' : [['x',' y',' z'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y',' x',' z+1/2']],
    '-P 4c 2' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y',' x',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2']],
    '-P 4c 2c' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y',' x',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    'P 4n 2c -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2']],
    '-P 4ac 2b' : [['x',' y',' z'],
              ['-y+1/2',' x',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z'],
              ['-x+1/2',' y',' -z'],
              ['y',' x',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z'],
              ['x+1/2',' -y',' z'],
              ['-y',' -x',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    'P 4n 2 -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    '-P 4ac 2bc' : [['x',' y',' z'],
              ['-y+1/2',' x',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['y',' x',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['-y',' -x',' z'],
              ['y+1/2',' x+1/2',' z']],
    '-P 4c 2ab' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y',' x',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    '-P 4n 2n' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y',' -x',' z'],
              ['y',' x',' z']],
    'P 4n 2n -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    '-P 4ac 2a' : [['x',' y',' z'],
              ['-y+1/2',' x',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z'],
              ['x',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y',' x',' z+1/2']],
    'P 4n 2ab -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    '-P 4ac 2ac' : [['x',' y',' z'],
              ['-y+1/2',' x',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y',' x',' z']],
    '-I 4 2' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2']],
    '-I 4 2c' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x',' y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z']],
    'I 4bw 2bw -1bw' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/4'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x',' -y+1/2',' -z+1/4'],
              ['-x',' y+1/2',' -z+1/4'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['x',' y+1/2',' -z+1/4'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['-y',' -x+1/2',' z+1/4'],
              ['y',' x+1/2',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' -z-1/4'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['x+1/2',' -y',' -z-1/4'],
              ['-x+1/2',' y',' -z-1/4'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y',' -z-1/4'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x',' z-1/4'],
              ['y+1/2',' x',' z-1/4']],
    '-I 4bd 2' : [['x',' y',' z'],
              ['-y+1/4',' x-1/4',' z+1/4'],
              ['-x',' -y+1/2',' z'],
              ['y+1/4',' -x+1/4',' z-1/4'],
              ['x',' -y',' -z'],
              ['-x',' y+1/2',' -z'],
              ['y+1/4',' x-1/4',' -z+1/4'],
              ['-y+1/4',' -x+1/4',' -z-1/4'],
              ['-x',' -y',' -z'],
              ['y-1/4',' -x+1/4',' -z-1/4'],
              ['x',' y+1/2',' -z'],
              ['-y-1/4',' x-1/4',' -z+1/4'],
              ['-x',' y',' z'],
              ['x',' -y+1/2',' z'],
              ['-y-1/4',' -x+1/4',' z-1/4'],
              ['y-1/4',' x-1/4',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['y-1/4',' x+1/4',' -z-1/4'],
              ['-y-1/4',' -x-1/4',' -z+1/4'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y+1/4',' -x-1/4',' -z+1/4'],
              ['x+1/2',' y',' -z+1/2'],
              ['-y+1/4',' x+1/4',' -z-1/4'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['-y+1/4',' -x-1/4',' z+1/4'],
              ['y+1/4',' x+1/4',' z-1/4']],
    'I 4bw 2aw -1bw' : [['x',' y',' z'],
              ['-x',' -y+1/2',' -z+1/4'],
              ['-y',' x+1/2',' z+1/4'],
              ['-x',' -y',' z'],
              ['y',' -x+1/2',' z+1/4'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['x+1/2',' -y',' -z+1/4'],
              ['-x+1/2',' y',' -z+1/4'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['x',' y+1/2',' -z+1/4'],
              ['-x',' y',' z+1/2'],
              ['x',' -y',' z+1/2'],
              ['-y+1/2',' -x',' z+1/4'],
              ['y+1/2',' x',' z+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -y',' -z-1/4'],
              ['-y+1/2',' x',' z-1/4'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x',' z-1/4'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['x',' -y+1/2',' -z-1/4'],
              ['-x',' y+1/2',' -z-1/4'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['x+1/2',' y',' -z-1/4'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z'],
              ['-y',' -x+1/2',' z-1/4'],
              ['y',' x+1/2',' z-1/4']],
    '-I 4bd 2c' : [['x',' y',' z'],
              ['-y+1/4',' x-1/4',' z+1/4'],
              ['-x',' -y+1/2',' z'],
              ['y+1/4',' -x+1/4',' z-1/4'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['y-1/4',' x+1/4',' -z+1/4'],
              ['-y+1/4',' -x+1/4',' -z+1/4'],
              ['-x',' -y',' -z'],
              ['y-1/4',' -x+1/4',' -z-1/4'],
              ['x',' y+1/2',' -z'],
              ['-y-1/4',' x-1/4',' -z+1/4'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z'],
              ['-y+1/4',' -x-1/4',' z-1/4'],
              ['y-1/4',' x-1/4',' z-1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['y+1/4',' x-1/4',' -z-1/4'],
              ['-y-1/4',' -x-1/4',' -z-1/4'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y+1/4',' -x-1/4',' -z+1/4'],
              ['x+1/2',' y',' -z+1/2'],
              ['-y+1/4',' x+1/4',' -z-1/4'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2'],
              ['-y-1/4',' -x+1/4',' z+1/4'],
              ['y+1/4',' x+1/4',' z+1/4']],
    'P 3' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z']],
    'P 31' : [['x',' y',' z'],
              ['-y',' x-y',' z+1/3'],
              ['-x+y',' -x',' z-1/3']],
    'P 32' : [['x',' y',' z'],
              ['-y',' x-y',' z-1/3'],
              ['-x+y',' -x',' z+1/3']],
    'R 3' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3']],
    'P 3*' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x']],
    '-P 3' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z']],
    '-R 3' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['-x-1/3',' -y+1/3',' -z+1/3'],
              ['y-1/3',' -x+y+1/3',' -z+1/3'],
              ['x-y-1/3',' x+1/3',' -z+1/3'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3'],
              ['-x+1/3',' -y-1/3',' -z-1/3'],
              ['y+1/3',' -x+y-1/3',' -z-1/3'],
              ['x-y+1/3',' x-1/3',' -z-1/3']],
    '-P 3*' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x']],
    'P 3 2' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z']],
    'P 3 2"' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z']],
    'P 31 2c (0 0 1)' : [['x',' y',' z'],
              ['-y',' x-y',' z+1/3'],
              ['-x+y',' -x',' z-1/3'],
              ['-y',' -x',' -z-1/3'],
              ['-x+y',' y',' -z+1/3'],
              ['x',' x-y',' -z']],
    'P 31 2"' : [['x',' y',' z'],
              ['-y',' x-y',' z+1/3'],
              ['-x+y',' -x',' z-1/3'],
              ['x-y',' -y',' -z-1/3'],
              ['-x',' -x+y',' -z+1/3'],
              ['y',' x',' -z']],
    'P 32 2c (0 0 -1)' : [['x',' y',' z'],
              ['-y',' x-y',' z-1/3'],
              ['-x+y',' -x',' z+1/3'],
              ['-y',' -x',' -z+1/3'],
              ['-x+y',' y',' -z-1/3'],
              ['x',' x-y',' -z']],
    'P 32 2"' : [['x',' y',' z'],
              ['-y',' x-y',' z-1/3'],
              ['-x+y',' -x',' z+1/3'],
              ['x-y',' -y',' -z+1/3'],
              ['-x',' -x+y',' -z-1/3'],
              ['y',' x',' -z']],
    'R 3 2"' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['x-y-1/3',' -y+1/3',' -z+1/3'],
              ['-x-1/3',' -x+y+1/3',' -z+1/3'],
              ['y-1/3',' x+1/3',' -z+1/3'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3'],
              ['x-y+1/3',' -y-1/3',' -z-1/3'],
              ['-x+1/3',' -x+y-1/3',' -z-1/3'],
              ['y+1/3',' x-1/3',' -z-1/3']],
    'P 3* 2' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -x',' -z'],
              ['-x',' -z',' -y'],
              ['-z',' -y',' -x']],
    'P 3 -2"' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z']],
    'P 3 -2' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    'P 3 -2"c' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2']],
    'P 3 -2c' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    'R 3 -2"' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['-x+y-1/3',' y+1/3',' z+1/3'],
              ['x-1/3',' x-y+1/3',' z+1/3'],
              ['-y-1/3',' -x+1/3',' z+1/3'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3'],
              ['-x+y+1/3',' y-1/3',' z-1/3'],
              ['x+1/3',' x-y-1/3',' z-1/3'],
              ['-y+1/3',' -x-1/3',' z-1/3']],
    'P 3* -2' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['y',' x',' z'],
              ['x',' z',' y'],
              ['z',' y',' x']],
    'R 3 -2"c' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['-x+y-1/3',' y+1/3',' z-1/6'],
              ['x-1/3',' x-y+1/3',' z-1/6'],
              ['-y-1/3',' -x+1/3',' z-1/6'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3'],
              ['-x+y+1/3',' y-1/3',' z+1/6'],
              ['x+1/3',' x-y-1/3',' z+1/6'],
              ['-y+1/3',' -x-1/3',' z+1/6']],
    'P 3* -2n' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    '-P 3 2' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    '-P 3 2c' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['-y',' -x',' -z+1/2'],
              ['-x+y',' y',' -z+1/2'],
              ['x',' x-y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    '-P 3 2"' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z']],
    '-P 3 2"c' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-y',' -y',' -z+1/2'],
              ['-x',' -x+y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2']],
    '-R 3 2"' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['x-y-1/3',' -y+1/3',' -z+1/3'],
              ['-x-1/3',' -x+y+1/3',' -z+1/3'],
              ['y-1/3',' x+1/3',' -z+1/3'],
              ['-x-1/3',' -y+1/3',' -z+1/3'],
              ['y-1/3',' -x+y+1/3',' -z+1/3'],
              ['x-y-1/3',' x+1/3',' -z+1/3'],
              ['-x+y-1/3',' y+1/3',' z+1/3'],
              ['x-1/3',' x-y+1/3',' z+1/3'],
              ['-y-1/3',' -x+1/3',' z+1/3'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3'],
              ['x-y+1/3',' -y-1/3',' -z-1/3'],
              ['-x+1/3',' -x+y-1/3',' -z-1/3'],
              ['y+1/3',' x-1/3',' -z-1/3'],
              ['-x+1/3',' -y-1/3',' -z-1/3'],
              ['y+1/3',' -x+y-1/3',' -z-1/3'],
              ['x-y+1/3',' x-1/3',' -z-1/3'],
              ['-x+y+1/3',' y-1/3',' z-1/3'],
              ['x+1/3',' x-y-1/3',' z-1/3'],
              ['-y+1/3',' -x-1/3',' z-1/3']],
    '-P 3* 2' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -x',' -z'],
              ['-x',' -z',' -y'],
              ['-z',' -y',' -x'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' x',' z'],
              ['x',' z',' y'],
              ['z',' y',' x']],
    '-R 3 2"c' : [['x',' y',' z'],
              ['-y',' x-y',' z'],
              ['-x+y',' -x',' z'],
              ['x-y',' -y',' -z+1/2'],
              ['-x',' -x+y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x+y',' -z'],
              ['x-y',' x',' -z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['x-1/3',' y+1/3',' z+1/3'],
              ['-y-1/3',' x-y+1/3',' z+1/3'],
              ['-x+y-1/3',' -x+1/3',' z+1/3'],
              ['x-y-1/3',' -y+1/3',' -z-1/6'],
              ['-x-1/3',' -x+y+1/3',' -z-1/6'],
              ['y-1/3',' x+1/3',' -z-1/6'],
              ['-x-1/3',' -y+1/3',' -z+1/3'],
              ['y-1/3',' -x+y+1/3',' -z+1/3'],
              ['x-y-1/3',' x+1/3',' -z+1/3'],
              ['-x+y-1/3',' y+1/3',' z-1/6'],
              ['x-1/3',' x-y+1/3',' z-1/6'],
              ['-y-1/3',' -x+1/3',' z-1/6'],
              ['x+1/3',' y-1/3',' z-1/3'],
              ['-y+1/3',' x-y-1/3',' z-1/3'],
              ['-x+y+1/3',' -x-1/3',' z-1/3'],
              ['x-y+1/3',' -y-1/3',' -z+1/6'],
              ['-x+1/3',' -x+y-1/3',' -z+1/6'],
              ['y+1/3',' x-1/3',' -z+1/6'],
              ['-x+1/3',' -y-1/3',' -z-1/3'],
              ['y+1/3',' -x+y-1/3',' -z-1/3'],
              ['x-y+1/3',' x-1/3',' -z-1/3'],
              ['-x+y+1/3',' y-1/3',' z+1/6'],
              ['x+1/3',' x-y-1/3',' z+1/6'],
              ['-y+1/3',' -x-1/3',' z+1/6']],
    '-P 3* 2n' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    'P 6' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z']],
    'P 61' : [['x',' y',' z'],
              ['x-y',' x',' z+1/6'],
              ['-y',' x-y',' z+1/3'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z-1/3'],
              ['y',' -x+y',' z-1/6']],
    'P 65' : [['x',' y',' z'],
              ['x-y',' x',' z-1/6'],
              ['-y',' x-y',' z-1/3'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z+1/3'],
              ['y',' -x+y',' z+1/6']],
    'P 62' : [['x',' y',' z'],
              ['x-y',' x',' z+1/3'],
              ['-y',' x-y',' z-1/3'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z+1/3'],
              ['y',' -x+y',' z-1/3']],
    'P 64' : [['x',' y',' z'],
              ['x-y',' x',' z-1/3'],
              ['-y',' x-y',' z+1/3'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z-1/3'],
              ['y',' -x+y',' z+1/3']],
    'P 6c' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2']],
    'P -6' : [['x',' y',' z'],
              ['-x+y',' -x',' -z'],
              ['-y',' x-y',' z'],
              ['x',' y',' -z'],
              ['-x+y',' -x',' z'],
              ['-y',' x-y',' -z']],
    '-P 6' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z'],
              ['-x',' -y',' -z'],
              ['-x+y',' -x',' -z'],
              ['y',' -x+y',' -z'],
              ['x',' y',' -z'],
              ['x-y',' x',' -z'],
              ['-y',' x-y',' -z']],
    '-P 6c' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2'],
              ['-x',' -y',' -z'],
              ['-x+y',' -x',' -z+1/2'],
              ['y',' -x+y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x-y',' x',' -z'],
              ['-y',' x-y',' -z+1/2']],
    'P 6 2' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z']],
    'P 61 2 (0 0 -1)' : [['x',' y',' z'],
              ['x-y',' x',' z+1/6'],
              ['-y',' x-y',' z+1/3'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z-1/3'],
              ['y',' -x+y',' z-1/6'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z-1/3'],
              ['y',' x',' -z+1/3'],
              ['-y',' -x',' -z-1/6'],
              ['-x+y',' y',' -z+1/2'],
              ['x',' x-y',' -z+1/6']],
    'P 65 2 (0 0 1)' : [['x',' y',' z'],
              ['x-y',' x',' z-1/6'],
              ['-y',' x-y',' z-1/3'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z+1/3'],
              ['y',' -x+y',' z+1/6'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z+1/3'],
              ['y',' x',' -z-1/3'],
              ['-y',' -x',' -z+1/6'],
              ['-x+y',' y',' -z+1/2'],
              ['x',' x-y',' -z-1/6']],
    'P 62 2c (0 0 1)' : [['x',' y',' z'],
              ['x-y',' x',' z+1/3'],
              ['-y',' x-y',' z-1/3'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z+1/3'],
              ['y',' -x+y',' z-1/3'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z+1/3'],
              ['y',' x',' -z-1/3'],
              ['-y',' -x',' -z-1/3'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z+1/3']],
    'P 64 2c (0 0 -1)' : [['x',' y',' z'],
              ['x-y',' x',' z-1/3'],
              ['-y',' x-y',' z+1/3'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z-1/3'],
              ['y',' -x+y',' z+1/3'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z-1/3'],
              ['y',' x',' -z+1/3'],
              ['-y',' -x',' -z+1/3'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z-1/3']],
    'P 6c 2c' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z+1/2'],
              ['-x+y',' y',' -z+1/2'],
              ['x',' x-y',' -z+1/2']],
    'P 6 -2' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    'P 6 -2c' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    'P 6c -2' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    'P 6c -2c' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    'P -6 2' : [['x',' y',' z'],
              ['-x+y',' -x',' -z'],
              ['-y',' x-y',' z'],
              ['x',' y',' -z'],
              ['-x+y',' -x',' z'],
              ['-y',' x-y',' -z'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z']],
    'P -6c 2' : [['x',' y',' z'],
              ['-x+y',' -x',' -z+1/2'],
              ['-y',' x-y',' z'],
              ['x',' y',' -z+1/2'],
              ['-x+y',' -x',' z'],
              ['-y',' x-y',' -z+1/2'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2']],
    'P -6 -2' : [['x',' y',' z'],
              ['-x+y',' -x',' -z'],
              ['-y',' x-y',' z'],
              ['x',' y',' -z'],
              ['-x+y',' -x',' z'],
              ['-y',' x-y',' -z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    'P -6c -2c' : [['x',' y',' z'],
              ['-x+y',' -x',' -z+1/2'],
              ['-y',' x-y',' z'],
              ['x',' y',' -z+1/2'],
              ['-x+y',' -x',' z'],
              ['-y',' x-y',' -z+1/2'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    '-P 6 2' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z'],
              ['-x',' -y',' -z'],
              ['-x+y',' -x',' -z'],
              ['y',' -x+y',' -z'],
              ['x',' y',' -z'],
              ['x-y',' x',' -z'],
              ['-y',' x-y',' -z'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    '-P 6 2c' : [['x',' y',' z'],
              ['x-y',' x',' z'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z'],
              ['x-y',' -y',' -z+1/2'],
              ['-x',' -x+y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x+y',' y',' -z+1/2'],
              ['x',' x-y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x+y',' -x',' -z'],
              ['y',' -x+y',' -z'],
              ['x',' y',' -z'],
              ['x-y',' x',' -z'],
              ['-y',' x-y',' -z'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    '-P 6c 2' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2'],
              ['x-y',' -y',' -z+1/2'],
              ['-x',' -x+y',' -z+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z'],
              ['-x+y',' y',' -z'],
              ['x',' x-y',' -z'],
              ['-x',' -y',' -z'],
              ['-x+y',' -x',' -z+1/2'],
              ['y',' -x+y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x-y',' x',' -z'],
              ['-y',' x-y',' -z+1/2'],
              ['-x+y',' y',' z+1/2'],
              ['x',' x-y',' z+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z'],
              ['x-y',' -y',' z'],
              ['-x',' -x+y',' z']],
    '-P 6c 2c' : [['x',' y',' z'],
              ['x-y',' x',' z+1/2'],
              ['-y',' x-y',' z'],
              ['-x',' -y',' z+1/2'],
              ['-x+y',' -x',' z'],
              ['y',' -x+y',' z+1/2'],
              ['x-y',' -y',' -z'],
              ['-x',' -x+y',' -z'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z+1/2'],
              ['-x+y',' y',' -z+1/2'],
              ['x',' x-y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-x+y',' -x',' -z+1/2'],
              ['y',' -x+y',' -z'],
              ['x',' y',' -z+1/2'],
              ['x-y',' x',' -z'],
              ['-y',' x-y',' -z+1/2'],
              ['-x+y',' y',' z'],
              ['x',' x-y',' z'],
              ['-y',' -x',' z'],
              ['y',' x',' z+1/2'],
              ['x-y',' -y',' z+1/2'],
              ['-x',' -x+y',' z+1/2']],
    'P 2 2 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z']],
    'F 2 2 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x',' y+1/2',' z+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z']],
    'I 2 2 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y+1/2'],
              ['-z+1/2',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2']],
    'P 2ac 2ab 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2']],
    'I 2b 2c 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z+1/2',' x'],
              ['z',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x'],
              ['-z',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y'],
              ['y',' -z',' -x+1/2'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2']],
    '-P 2 2 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z']],
    'P 2 2 3 -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' -y+1/2'],
              ['z+1/2',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x+1/2'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2ab 2bc 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y+1/2',' z+1/2',' -x'],
              ['-z',' x+1/2',' y+1/2'],
              ['y+1/2',' -z',' x+1/2'],
              ['z+1/2',' x+1/2',' -y'],
              ['z+1/2',' -x',' y+1/2'],
              ['-y',' z+1/2',' x+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x',' y+1/2',' z+1/2'],
              ['x+1/2',' -y',' z+1/2']],
    '-F 2 2 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x',' y+1/2',' z+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-z',' -x+1/2',' -y+1/2'],
              ['-y',' -z+1/2',' -x+1/2'],
              ['y',' z+1/2',' -x+1/2'],
              ['-z',' x+1/2',' y+1/2'],
              ['y',' -z+1/2',' x+1/2'],
              ['z',' x+1/2',' -y+1/2'],
              ['z',' -x+1/2',' y+1/2'],
              ['-y',' z+1/2',' x+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' -z',' -x+1/2'],
              ['y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' x',' y+1/2'],
              ['y+1/2',' -z',' x+1/2'],
              ['z+1/2',' x',' -y+1/2'],
              ['z+1/2',' -x',' y+1/2'],
              ['-y+1/2',' z',' x+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' -z+1/2',' -x'],
              ['y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' x+1/2',' y'],
              ['y+1/2',' -z+1/2',' x'],
              ['z+1/2',' x+1/2',' -y'],
              ['z+1/2',' -x+1/2',' y'],
              ['-y+1/2',' z+1/2',' x'],
              ['x+1/2',' y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' z'],
              ['x+1/2',' -y+1/2',' z']],
    'F 2 2 3 -1d' : [['x',' y',' z'],
              ['-x+1/4',' -y+1/4',' -z+1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-z+1/4',' -x+1/4',' -y+1/4'],
              ['-y+1/4',' -z+1/4',' -x+1/4'],
              ['y+1/4',' z+1/4',' -x+1/4'],
              ['-z+1/4',' x+1/4',' y+1/4'],
              ['y+1/4',' -z+1/4',' x+1/4'],
              ['z+1/4',' x+1/4',' -y+1/4'],
              ['z+1/4',' -x+1/4',' y+1/4'],
              ['-y+1/4',' z+1/4',' x+1/4'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['x+1/4',' y+1/4',' -z+1/4'],
              ['-x+1/4',' y+1/4',' z+1/4'],
              ['x+1/4',' -y+1/4',' z+1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/4',' -y-1/4',' -z-1/4'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-z+1/4',' -x-1/4',' -y-1/4'],
              ['-y+1/4',' -z-1/4',' -x-1/4'],
              ['y+1/4',' z-1/4',' -x-1/4'],
              ['-z+1/4',' x-1/4',' y-1/4'],
              ['y+1/4',' -z-1/4',' x-1/4'],
              ['z+1/4',' x-1/4',' -y-1/4'],
              ['z+1/4',' -x-1/4',' y-1/4'],
              ['-y+1/4',' z-1/4',' x-1/4'],
              ['-x',' -y+1/2',' z+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['x+1/4',' y-1/4',' -z-1/4'],
              ['-x+1/4',' y-1/4',' z-1/4'],
              ['x+1/4',' -y-1/4',' z-1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['-x-1/4',' -y+1/4',' -z-1/4'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-z-1/4',' -x+1/4',' -y-1/4'],
              ['-y-1/4',' -z+1/4',' -x-1/4'],
              ['y-1/4',' z+1/4',' -x-1/4'],
              ['-z-1/4',' x+1/4',' y-1/4'],
              ['y-1/4',' -z+1/4',' x-1/4'],
              ['z-1/4',' x+1/4',' -y-1/4'],
              ['z-1/4',' -x+1/4',' y-1/4'],
              ['-y-1/4',' z+1/4',' x-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['x-1/4',' y+1/4',' -z-1/4'],
              ['-x-1/4',' y+1/4',' z-1/4'],
              ['x-1/4',' -y+1/4',' z-1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['-x-1/4',' -y-1/4',' -z+1/4'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-z-1/4',' -x-1/4',' -y+1/4'],
              ['-y-1/4',' -z-1/4',' -x+1/4'],
              ['y-1/4',' z-1/4',' -x+1/4'],
              ['-z-1/4',' x-1/4',' y+1/4'],
              ['y-1/4',' -z-1/4',' x+1/4'],
              ['z-1/4',' x-1/4',' -y+1/4'],
              ['z-1/4',' -x-1/4',' y+1/4'],
              ['-y-1/4',' z-1/4',' x+1/4'],
              ['-x+1/2',' -y+1/2',' z'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' y+1/2',' -z'],
              ['x-1/4',' y-1/4',' -z+1/4'],
              ['-x-1/4',' y-1/4',' z+1/4'],
              ['x-1/4',' -y-1/4',' z+1/4']],
    '-F 2uv 2vw 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/4',' -z+1/4',' x'],
              ['z',' -x+1/4',' -y+1/4'],
              ['-y+1/4',' z',' -x+1/4'],
              ['-z+1/4',' -x+1/4',' y'],
              ['-z+1/4',' x',' -y+1/4'],
              ['y',' -z+1/4',' -x+1/4'],
              ['-x+1/4',' -y+1/4',' z'],
              ['x',' -y+1/4',' -z+1/4'],
              ['-x+1/4',' y',' -z+1/4'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y-1/4',' z-1/4',' -x'],
              ['-z',' x-1/4',' y-1/4'],
              ['y-1/4',' -z',' x-1/4'],
              ['z-1/4',' x-1/4',' -y'],
              ['z-1/4',' -x',' y-1/4'],
              ['-y',' z-1/4',' x-1/4'],
              ['x-1/4',' y-1/4',' -z'],
              ['-x',' y-1/4',' z-1/4'],
              ['x-1/4',' -y',' z-1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y+1/4',' -z-1/4',' x+1/2'],
              ['z',' -x-1/4',' -y-1/4'],
              ['-y+1/4',' z+1/2',' -x-1/4'],
              ['-z+1/4',' -x-1/4',' y+1/2'],
              ['-z+1/4',' x+1/2',' -y-1/4'],
              ['y',' -z-1/4',' -x-1/4'],
              ['-x+1/4',' -y-1/4',' z+1/2'],
              ['x',' -y-1/4',' -z-1/4'],
              ['-x+1/4',' y+1/2',' -z-1/4'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['-z',' -x+1/2',' -y+1/2'],
              ['-y',' -z+1/2',' -x+1/2'],
              ['y-1/4',' z+1/4',' -x+1/2'],
              ['-z',' x+1/4',' y+1/4'],
              ['y-1/4',' -z+1/2',' x+1/4'],
              ['z-1/4',' x+1/4',' -y+1/2'],
              ['z-1/4',' -x+1/2',' y+1/4'],
              ['-y',' z+1/4',' x+1/4'],
              ['x-1/4',' y+1/4',' -z+1/2'],
              ['-x',' y+1/4',' z+1/4'],
              ['x-1/4',' -y+1/2',' z+1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y-1/4',' -z+1/4',' x+1/2'],
              ['z+1/2',' -x+1/4',' -y-1/4'],
              ['-y-1/4',' z',' -x-1/4'],
              ['-z-1/4',' -x+1/4',' y+1/2'],
              ['-z-1/4',' x',' -y-1/4'],
              ['y+1/2',' -z+1/4',' -x-1/4'],
              ['-x-1/4',' -y+1/4',' z+1/2'],
              ['x+1/2',' -y+1/4',' -z-1/4'],
              ['-x-1/4',' y',' -z-1/4'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['-z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' -z',' -x+1/2'],
              ['y+1/4',' z-1/4',' -x+1/2'],
              ['-z+1/2',' x-1/4',' y+1/4'],
              ['y+1/4',' -z',' x+1/4'],
              ['z+1/4',' x-1/4',' -y+1/2'],
              ['z+1/4',' -x',' y+1/4'],
              ['-y+1/2',' z-1/4',' x+1/4'],
              ['x+1/4',' y-1/4',' -z+1/2'],
              ['-x+1/2',' y-1/4',' z+1/4'],
              ['x+1/4',' -y',' z+1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y-1/4',' -z-1/4',' x'],
              ['z+1/2',' -x-1/4',' -y+1/4'],
              ['-y-1/4',' z+1/2',' -x+1/4'],
              ['-z-1/4',' -x-1/4',' y'],
              ['-z-1/4',' x+1/2',' -y+1/4'],
              ['y+1/2',' -z-1/4',' -x+1/4'],
              ['-x-1/4',' -y-1/4',' z'],
              ['x+1/2',' -y-1/4',' -z+1/4'],
              ['-x-1/4',' y+1/2',' -z+1/4'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['-z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' -z+1/2',' -x'],
              ['y+1/4',' z+1/4',' -x'],
              ['-z+1/2',' x+1/4',' y-1/4'],
              ['y+1/4',' -z+1/2',' x-1/4'],
              ['z+1/4',' x+1/4',' -y'],
              ['z+1/4',' -x+1/2',' y-1/4'],
              ['-y+1/2',' z+1/4',' x-1/4'],
              ['x+1/4',' y+1/4',' -z'],
              ['-x+1/2',' y+1/4',' z-1/4'],
              ['x+1/4',' -y+1/2',' z-1/4']],
    '-I 2 2 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-x',' -y',' z'],
              ['x',' -y',' -z'],
              ['-x',' y',' -z'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['x',' y',' -z'],
              ['-x',' y',' z'],
              ['x',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y+1/2'],
              ['-z+1/2',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' -y+1/2'],
              ['z+1/2',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2']],
    '-P 2ac 2ab 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y'],
              ['y',' -z+1/2',' x+1/2'],
              ['z+1/2',' x',' -y+1/2'],
              ['z',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    '-I 2b 2c 3' : [['x',' y',' z'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z+1/2',' x'],
              ['z',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x'],
              ['-z',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y'],
              ['y',' -z',' -x+1/2'],
              ['-x',' -y+1/2',' z'],
              ['x',' -y',' -z+1/2'],
              ['-x+1/2',' y',' -z'],
              ['-x',' -y',' -z'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z+1/2',' -x'],
              ['-z',' x',' y+1/2'],
              ['y+1/2',' -z',' x'],
              ['z',' x+1/2',' -y'],
              ['z+1/2',' -x',' y'],
              ['-y',' z',' x+1/2'],
              ['x',' y+1/2',' -z'],
              ['-x',' y',' z+1/2'],
              ['x+1/2',' -y',' z'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-x+1/2',' -y',' z+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y'],
              ['y',' -z+1/2',' x+1/2'],
              ['z+1/2',' x',' -y+1/2'],
              ['z',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x'],
              ['x+1/2',' y',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['x',' -y+1/2',' z+1/2']],
    'P 4 2 3' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x']],
    'P 4n 2 3' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' y+1/2'],
              ['x',' -y',' -z'],
              ['x+1/2',' z+1/2',' -y+1/2'],
              ['z+1/2',' y+1/2',' -x+1/2'],
              ['-x',' y',' -z'],
              ['-z+1/2',' y+1/2',' x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' y+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z+1/2',' -y+1/2',' x+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2']],
    'F 4 2 3' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x'],
              ['x',' y+1/2',' z+1/2'],
              ['-y',' x+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['y',' -x+1/2',' z+1/2'],
              ['x',' -z+1/2',' y+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x',' z+1/2',' -y+1/2'],
              ['z',' y+1/2',' -x+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z',' y+1/2',' x+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['y',' x+1/2',' -z+1/2'],
              ['-y',' -x+1/2',' -z+1/2'],
              ['-x',' z+1/2',' y+1/2'],
              ['-x',' -z+1/2',' -y+1/2'],
              ['z',' -y+1/2',' x+1/2'],
              ['-z',' -y+1/2',' -x+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-y+1/2',' x',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y+1/2',' -x',' z+1/2'],
              ['x+1/2',' -z',' y+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' z',' -y+1/2'],
              ['z+1/2',' y',' -x+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z+1/2',' y',' x+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['y+1/2',' x',' -z+1/2'],
              ['-y+1/2',' -x',' -z+1/2'],
              ['-x+1/2',' z',' y+1/2'],
              ['-x+1/2',' -z',' -y+1/2'],
              ['z+1/2',' -y',' x+1/2'],
              ['-z+1/2',' -y',' -x+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-y+1/2',' x+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y+1/2',' -x+1/2',' z'],
              ['x+1/2',' -z+1/2',' y'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' z+1/2',' -y'],
              ['z+1/2',' y+1/2',' -x'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-z+1/2',' y+1/2',' x'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' z+1/2',' y'],
              ['-x+1/2',' -z+1/2',' -y'],
              ['z+1/2',' -y+1/2',' x'],
              ['-z+1/2',' -y+1/2',' -x']],
    'F 4d 2 3' : [['x',' y',' z'],
              ['-y+1/4',' x+1/4',' z+1/4'],
              ['-x',' -y',' z'],
              ['y+1/4',' -x+1/4',' z+1/4'],
              ['x+1/4',' -z+1/4',' y+1/4'],
              ['x',' -y',' -z'],
              ['x+1/4',' z+1/4',' -y+1/4'],
              ['z+1/4',' y+1/4',' -x+1/4'],
              ['-x',' y',' -z'],
              ['-z+1/4',' y+1/4',' x+1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y+1/4',' x+1/4',' -z+1/4'],
              ['-y+1/4',' -x+1/4',' -z+1/4'],
              ['-x+1/4',' z+1/4',' y+1/4'],
              ['-x+1/4',' -z+1/4',' -y+1/4'],
              ['z+1/4',' -y+1/4',' x+1/4'],
              ['-z+1/4',' -y+1/4',' -x+1/4'],
              ['x',' y+1/2',' z+1/2'],
              ['-y+1/4',' x-1/4',' z-1/4'],
              ['-x',' -y+1/2',' z+1/2'],
              ['y+1/4',' -x-1/4',' z-1/4'],
              ['x+1/4',' -z-1/4',' y-1/4'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x+1/4',' z-1/4',' -y-1/4'],
              ['z+1/4',' y-1/4',' -x-1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z+1/4',' y-1/4',' x-1/4'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['y+1/4',' x-1/4',' -z-1/4'],
              ['-y+1/4',' -x-1/4',' -z-1/4'],
              ['-x+1/4',' z-1/4',' y-1/4'],
              ['-x+1/4',' -z-1/4',' -y-1/4'],
              ['z+1/4',' -y-1/4',' x-1/4'],
              ['-z+1/4',' -y-1/4',' -x-1/4'],
              ['x+1/2',' y',' z+1/2'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x+1/4',' z-1/4'],
              ['x-1/4',' -z+1/4',' y-1/4'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x-1/4',' z+1/4',' -y-1/4'],
              ['z-1/4',' y+1/4',' -x-1/4'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z-1/4',' y+1/4',' x-1/4'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['y-1/4',' x+1/4',' -z-1/4'],
              ['-y-1/4',' -x+1/4',' -z-1/4'],
              ['-x-1/4',' z+1/4',' y-1/4'],
              ['-x-1/4',' -z+1/4',' -y-1/4'],
              ['z-1/4',' -y+1/4',' x-1/4'],
              ['-z-1/4',' -y+1/4',' -x-1/4'],
              ['x+1/2',' y+1/2',' z'],
              ['-y-1/4',' x-1/4',' z+1/4'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x-1/4',' -z-1/4',' y+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x-1/4',' z-1/4',' -y+1/4'],
              ['z-1/4',' y-1/4',' -x+1/4'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-z-1/4',' y-1/4',' x+1/4'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y-1/4',' x-1/4',' -z+1/4'],
              ['-y-1/4',' -x-1/4',' -z+1/4'],
              ['-x-1/4',' z-1/4',' y+1/4'],
              ['-x-1/4',' -z-1/4',' -y+1/4'],
              ['z-1/4',' -y-1/4',' x+1/4'],
              ['-z-1/4',' -y-1/4',' -x+1/4']],
    'I 4 2 3' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' y+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' z+1/2',' -y+1/2'],
              ['z+1/2',' y+1/2',' -x+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-z+1/2',' y+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y+1/2'],
              ['-z+1/2',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' y+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z+1/2',' -y+1/2',' x+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2']],
    'P 4acd 2ab 3' : [['x',' y',' z'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x-1/4',' -z-1/4',' y+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/4',' z-1/4',' -y-1/4'],
              ['z+1/4',' y-1/4',' -x-1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z-1/4',' y+1/4',' x-1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y+1/4',' x-1/4',' -z-1/4'],
              ['-y+1/4',' -x+1/4',' -z+1/4'],
              ['-x-1/4',' z+1/4',' y-1/4'],
              ['-x+1/4',' -z+1/4',' -y+1/4'],
              ['z-1/4',' -y-1/4',' x+1/4'],
              ['-z+1/4',' -y+1/4',' -x+1/4']],
    'P 4bd 2ab 3' : [['x',' y',' z'],
              ['-y+1/4',' x-1/4',' z+1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y+1/4',' -x+1/4',' z-1/4'],
              ['x+1/4',' -z+1/4',' y-1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x-1/4',' z+1/4',' -y+1/4'],
              ['z-1/4',' y+1/4',' -x+1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z+1/4',' y-1/4',' x+1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y-1/4',' x+1/4',' -z+1/4'],
              ['-y-1/4',' -x-1/4',' -z-1/4'],
              ['-x+1/4',' z-1/4',' y+1/4'],
              ['-x-1/4',' -z-1/4',' -y-1/4'],
              ['z+1/4',' -y+1/4',' x-1/4'],
              ['-z-1/4',' -y-1/4',' -x-1/4']],
    'I 4bd 2c 3' : [['x',' y',' z'],
              ['-y+1/4',' x-1/4',' z+1/4'],
              ['-x',' -y+1/2',' z'],
              ['y+1/4',' -x+1/4',' z-1/4'],
              ['x+1/4',' -z+1/4',' y-1/4'],
              ['x',' -y',' -z+1/2'],
              ['x-1/4',' z+1/4',' -y+1/4'],
              ['z-1/4',' y+1/4',' -x+1/4'],
              ['-x+1/2',' y',' -z'],
              ['-z+1/4',' y-1/4',' x+1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z+1/2',' x'],
              ['z',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x'],
              ['-z',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y'],
              ['y',' -z',' -x+1/2'],
              ['y-1/4',' x+1/4',' -z+1/4'],
              ['-y+1/4',' -x+1/4',' -z+1/4'],
              ['-x+1/4',' z-1/4',' y+1/4'],
              ['-x+1/4',' -z+1/4',' -y+1/4'],
              ['z+1/4',' -y+1/4',' x-1/4'],
              ['-z+1/4',' -y+1/4',' -x+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x-1/4',' -z-1/4',' y+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/4',' z-1/4',' -y-1/4'],
              ['z+1/4',' y-1/4',' -x-1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z-1/4',' y+1/4',' x-1/4'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y+1/4',' x-1/4',' -z-1/4'],
              ['-y-1/4',' -x-1/4',' -z-1/4'],
              ['-x-1/4',' z+1/4',' y-1/4'],
              ['-x-1/4',' -z-1/4',' -y-1/4'],
              ['z-1/4',' -y-1/4',' x+1/4'],
              ['-z-1/4',' -y-1/4',' -x-1/4']],
    'P -4 2 3' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['x',' -y',' -z'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['-x',' y',' -z'],
              ['z',' -y',' -x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x']],
    'F -4 2 3' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['x',' -y',' -z'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['-x',' y',' -z'],
              ['z',' -y',' -x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x'],
              ['x',' y+1/2',' z+1/2'],
              ['y',' -x+1/2',' -z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x',' z+1/2',' -y+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' -z+1/2',' y+1/2'],
              ['-z',' -y+1/2',' x+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['z',' -y+1/2',' -x+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-y',' -x+1/2',' z+1/2'],
              ['y',' x+1/2',' z+1/2'],
              ['x',' -z+1/2',' -y+1/2'],
              ['x',' z+1/2',' y+1/2'],
              ['-z',' y+1/2',' -x+1/2'],
              ['z',' y+1/2',' x+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['y+1/2',' -x',' -z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-y+1/2',' x',' -z+1/2'],
              ['-x+1/2',' z',' -y+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -z',' y+1/2'],
              ['-z+1/2',' -y',' x+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['z+1/2',' -y',' -x+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-y+1/2',' -x',' z+1/2'],
              ['y+1/2',' x',' z+1/2'],
              ['x+1/2',' -z',' -y+1/2'],
              ['x+1/2',' z',' y+1/2'],
              ['-z+1/2',' y',' -x+1/2'],
              ['z+1/2',' y',' x+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' x+1/2',' -z'],
              ['-x+1/2',' z+1/2',' -y'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -z+1/2',' y'],
              ['-z+1/2',' -y+1/2',' x'],
              ['-x+1/2',' y+1/2',' -z'],
              ['z+1/2',' -y+1/2',' -x'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z'],
              ['x+1/2',' -z+1/2',' -y'],
              ['x+1/2',' z+1/2',' y'],
              ['-z+1/2',' y+1/2',' -x'],
              ['z+1/2',' y+1/2',' x']],
    'I -4 2 3' : [['x',' y',' z'],
              ['y',' -x',' -z'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['x',' -y',' -z'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['-x',' y',' -z'],
              ['z',' -y',' -x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y+1/2'],
              ['-z+1/2',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    'P -4n 2 3' : [['x',' y',' z'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x',' -y',' z'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['x',' -y',' -z'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['-x',' y',' -z'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    'F -4c 2 3' : [['x',' y',' z'],
              ['y',' -x',' -z+1/2'],
              ['-x',' -y',' z'],
              ['-y',' x',' -z+1/2'],
              ['-x',' z',' -y+1/2'],
              ['x',' -y',' -z'],
              ['-x',' -z',' y+1/2'],
              ['-z',' -y',' x+1/2'],
              ['-x',' y',' -z'],
              ['z',' -y',' -x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x',' -z',' -y+1/2'],
              ['x',' z',' y+1/2'],
              ['-z',' y',' -x+1/2'],
              ['z',' y',' x+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['y',' -x+1/2',' -z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['-y',' x+1/2',' -z'],
              ['-x',' z+1/2',' -y'],
              ['x',' -y+1/2',' -z+1/2'],
              ['-x',' -z+1/2',' y'],
              ['-z',' -y+1/2',' x'],
              ['-x',' y+1/2',' -z+1/2'],
              ['z',' -y+1/2',' -x'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-y',' -x+1/2',' z'],
              ['y',' x+1/2',' z'],
              ['x',' -z+1/2',' -y'],
              ['x',' z+1/2',' y'],
              ['-z',' y+1/2',' -x'],
              ['z',' y+1/2',' x'],
              ['x+1/2',' y',' z+1/2'],
              ['y+1/2',' -x',' -z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-y+1/2',' x',' -z'],
              ['-x+1/2',' z',' -y'],
              ['x+1/2',' -y',' -z+1/2'],
              ['-x+1/2',' -z',' y'],
              ['-z+1/2',' -y',' x'],
              ['-x+1/2',' y',' -z+1/2'],
              ['z+1/2',' -y',' -x'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-y+1/2',' -x',' z'],
              ['y+1/2',' x',' z'],
              ['x+1/2',' -z',' -y'],
              ['x+1/2',' z',' y'],
              ['-z+1/2',' y',' -x'],
              ['z+1/2',' y',' x'],
              ['x+1/2',' y+1/2',' z'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    'I -4bd 2c 3' : [['x',' y',' z'],
              ['y+1/4',' -x-1/4',' -z+1/4'],
              ['-x',' -y+1/2',' z'],
              ['-y+1/4',' x+1/4',' -z-1/4'],
              ['-x+1/4',' z+1/4',' -y-1/4'],
              ['x',' -y',' -z+1/2'],
              ['-x-1/4',' -z+1/4',' y+1/4'],
              ['-z-1/4',' -y+1/4',' x+1/4'],
              ['-x+1/2',' y',' -z'],
              ['z+1/4',' -y-1/4',' -x+1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z+1/2',' x'],
              ['z',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x'],
              ['-z',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y'],
              ['y',' -z',' -x+1/2'],
              ['-y-1/4',' -x+1/4',' z+1/4'],
              ['y+1/4',' x+1/4',' z+1/4'],
              ['x+1/4',' -z-1/4',' -y+1/4'],
              ['x+1/4',' z+1/4',' y+1/4'],
              ['-z+1/4',' y+1/4',' -x-1/4'],
              ['z+1/4',' y+1/4',' x+1/4'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['y-1/4',' -x+1/4',' -z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['-y-1/4',' x-1/4',' -z+1/4'],
              ['-x-1/4',' z-1/4',' -y+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['-x+1/4',' -z-1/4',' y-1/4'],
              ['-z+1/4',' -y-1/4',' x-1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['z-1/4',' -y+1/4',' -x-1/4'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-y+1/4',' -x-1/4',' z-1/4'],
              ['y-1/4',' x-1/4',' z-1/4'],
              ['x-1/4',' -z+1/4',' -y-1/4'],
              ['x-1/4',' z-1/4',' y-1/4'],
              ['-z-1/4',' y-1/4',' -x+1/4'],
              ['z-1/4',' y-1/4',' x-1/4']],
    '-P 4 2 3' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['-x',' y',' z'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['x',' -y',' z'],
              ['z',' -y',' -x'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x']],
    'P 4 2 3 -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' -y+1/2'],
              ['z+1/2',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x+1/2'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    '-P 4a 2bc 3' : [['x',' y',' z'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y',' -x+1/2',' z'],
              ['x',' -z+1/2',' y'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x',' z',' -y+1/2'],
              ['z',' y',' -x+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z+1/2',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['y',' x',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z',' y'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z',' -y+1/2',' x'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y',' x+1/2',' -z'],
              ['-x',' z+1/2',' -y'],
              ['-x',' y+1/2',' z+1/2'],
              ['-x',' -z',' y+1/2'],
              ['-z',' -y',' x+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['z+1/2',' -y',' -x'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y+1/2',' z+1/2',' -x'],
              ['-z',' x+1/2',' y+1/2'],
              ['y+1/2',' -z',' x+1/2'],
              ['z+1/2',' x+1/2',' -y'],
              ['z+1/2',' -x',' y+1/2'],
              ['-y',' z+1/2',' x+1/2'],
              ['-y',' -x',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z',' -y'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z',' y+1/2',' -x'],
              ['z+1/2',' y+1/2',' x+1/2']],
    '-P 4n 2 3' : [['x',' y',' z'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' y+1/2'],
              ['x',' -y',' -z'],
              ['x+1/2',' z+1/2',' -y+1/2'],
              ['z+1/2',' y+1/2',' -x+1/2'],
              ['-x',' y',' -z'],
              ['-z+1/2',' y+1/2',' x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' y+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z+1/2',' -y+1/2',' x+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['-x',' -y',' -z'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['-x',' y',' z'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['x',' -y',' z'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    'P 4n 2 3 -1n' : [['x',' y',' z'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x',' -y',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' y+1/2'],
              ['x',' -y',' -z'],
              ['x+1/2',' z+1/2',' -y+1/2'],
              ['z+1/2',' y+1/2',' -x+1/2'],
              ['-x',' y',' -z'],
              ['-z+1/2',' y+1/2',' x+1/2'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['z',' -y',' -x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' -y+1/2'],
              ['z+1/2',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' y+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z+1/2',' -y+1/2',' x+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x']],
    '-P 4bc 2bc 3' : [['x',' y',' z'],
              ['-y',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y+1/2',' -x',' z+1/2'],
              ['x+1/2',' -z',' y+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x+1/2',' z+1/2',' -y'],
              ['z+1/2',' y+1/2',' -x'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z',' y+1/2',' x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z+1/2',' y+1/2'],
              ['-x',' -z',' -y'],
              ['z+1/2',' -y',' x+1/2'],
              ['-z',' -y',' -x'],
              ['-x',' -y',' -z'],
              ['y',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y+1/2',' x',' -z+1/2'],
              ['-x+1/2',' z',' -y+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['-x+1/2',' -z+1/2',' y'],
              ['-z+1/2',' -y+1/2',' x'],
              ['x+1/2',' -y',' z+1/2'],
              ['z',' -y+1/2',' -x+1/2'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y+1/2',' z+1/2',' -x'],
              ['-z',' x+1/2',' y+1/2'],
              ['y+1/2',' -z',' x+1/2'],
              ['z+1/2',' x+1/2',' -y'],
              ['z+1/2',' -x',' y+1/2'],
              ['-y',' z+1/2',' x+1/2'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y',' x',' z'],
              ['x',' -z+1/2',' -y+1/2'],
              ['x',' z',' y'],
              ['-z+1/2',' y',' -x+1/2'],
              ['z',' y',' x']],
    '-F 4 2 3' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['-x',' y',' z'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['x',' -y',' z'],
              ['z',' -y',' -x'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x'],
              ['x',' y+1/2',' z+1/2'],
              ['-y',' x+1/2',' z+1/2'],
              ['-x',' -y+1/2',' z+1/2'],
              ['y',' -x+1/2',' z+1/2'],
              ['x',' -z+1/2',' y+1/2'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x',' z+1/2',' -y+1/2'],
              ['z',' y+1/2',' -x+1/2'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z',' y+1/2',' x+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['y',' x+1/2',' -z+1/2'],
              ['-y',' -x+1/2',' -z+1/2'],
              ['-x',' z+1/2',' y+1/2'],
              ['-x',' -z+1/2',' -y+1/2'],
              ['z',' -y+1/2',' x+1/2'],
              ['-z',' -y+1/2',' -x+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['y',' -x+1/2',' -z+1/2'],
              ['x',' y+1/2',' -z+1/2'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x',' z+1/2',' -y+1/2'],
              ['-x',' y+1/2',' z+1/2'],
              ['-x',' -z+1/2',' y+1/2'],
              ['-z',' -y+1/2',' x+1/2'],
              ['x',' -y+1/2',' z+1/2'],
              ['z',' -y+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' -y+1/2'],
              ['-y',' -z+1/2',' -x+1/2'],
              ['y',' z+1/2',' -x+1/2'],
              ['-z',' x+1/2',' y+1/2'],
              ['y',' -z+1/2',' x+1/2'],
              ['z',' x+1/2',' -y+1/2'],
              ['z',' -x+1/2',' y+1/2'],
              ['-y',' z+1/2',' x+1/2'],
              ['-y',' -x+1/2',' z+1/2'],
              ['y',' x+1/2',' z+1/2'],
              ['x',' -z+1/2',' -y+1/2'],
              ['x',' z+1/2',' y+1/2'],
              ['-z',' y+1/2',' -x+1/2'],
              ['z',' y+1/2',' x+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-y+1/2',' x',' z+1/2'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y+1/2',' -x',' z+1/2'],
              ['x+1/2',' -z',' y+1/2'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' z',' -y+1/2'],
              ['z+1/2',' y',' -x+1/2'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z+1/2',' y',' x+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['y+1/2',' x',' -z+1/2'],
              ['-y+1/2',' -x',' -z+1/2'],
              ['-x+1/2',' z',' y+1/2'],
              ['-x+1/2',' -z',' -y+1/2'],
              ['z+1/2',' -y',' x+1/2'],
              ['-z+1/2',' -y',' -x+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['y+1/2',' -x',' -z+1/2'],
              ['x+1/2',' y',' -z+1/2'],
              ['-y+1/2',' x',' -z+1/2'],
              ['-x+1/2',' z',' -y+1/2'],
              ['-x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -z',' y+1/2'],
              ['-z+1/2',' -y',' x+1/2'],
              ['x+1/2',' -y',' z+1/2'],
              ['z+1/2',' -y',' -x+1/2'],
              ['-z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' -z',' -x+1/2'],
              ['y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' x',' y+1/2'],
              ['y+1/2',' -z',' x+1/2'],
              ['z+1/2',' x',' -y+1/2'],
              ['z+1/2',' -x',' y+1/2'],
              ['-y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -x',' z+1/2'],
              ['y+1/2',' x',' z+1/2'],
              ['x+1/2',' -z',' -y+1/2'],
              ['x+1/2',' z',' y+1/2'],
              ['-z+1/2',' y',' -x+1/2'],
              ['z+1/2',' y',' x+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-y+1/2',' x+1/2',' z'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y+1/2',' -x+1/2',' z'],
              ['x+1/2',' -z+1/2',' y'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' z+1/2',' -y'],
              ['z+1/2',' y+1/2',' -x'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-z+1/2',' y+1/2',' x'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y+1/2',' x+1/2',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' z+1/2',' y'],
              ['-x+1/2',' -z+1/2',' -y'],
              ['z+1/2',' -y+1/2',' x'],
              ['-z+1/2',' -y+1/2',' -x'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['y+1/2',' -x+1/2',' -z'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y+1/2',' x+1/2',' -z'],
              ['-x+1/2',' z+1/2',' -y'],
              ['-x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -z+1/2',' y'],
              ['-z+1/2',' -y+1/2',' x'],
              ['x+1/2',' -y+1/2',' z'],
              ['z+1/2',' -y+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' -z+1/2',' -x'],
              ['y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' x+1/2',' y'],
              ['y+1/2',' -z+1/2',' x'],
              ['z+1/2',' x+1/2',' -y'],
              ['z+1/2',' -x+1/2',' y'],
              ['-y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z'],
              ['x+1/2',' -z+1/2',' -y'],
              ['x+1/2',' z+1/2',' y'],
              ['-z+1/2',' y+1/2',' -x'],
              ['z+1/2',' y+1/2',' x']],
    '-F 4c 2 3' : [['x',' y',' z'],
              ['-y',' x',' z+1/2'],
              ['-x',' -y',' z'],
              ['y',' -x',' z+1/2'],
              ['x',' -z',' y+1/2'],
              ['x',' -y',' -z'],
              ['x',' z',' -y+1/2'],
              ['z',' y',' -x+1/2'],
              ['-x',' y',' -z'],
              ['-z',' y',' x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z+1/2'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' z',' y+1/2'],
              ['-x',' -z',' -y+1/2'],
              ['z',' -y',' x+1/2'],
              ['-z',' -y',' -x+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z+1/2'],
              ['x',' y',' -z'],
              ['-y',' x',' -z+1/2'],
              ['-x',' z',' -y+1/2'],
              ['-x',' y',' z'],
              ['-x',' -z',' y+1/2'],
              ['-z',' -y',' x+1/2'],
              ['x',' -y',' z'],
              ['z',' -y',' -x+1/2'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x',' -z',' -y+1/2'],
              ['x',' z',' y+1/2'],
              ['-z',' y',' -x+1/2'],
              ['z',' y',' x+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-y',' x+1/2',' z'],
              ['-x',' -y+1/2',' z+1/2'],
              ['y',' -x+1/2',' z'],
              ['x',' -z+1/2',' y'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x',' z+1/2',' -y'],
              ['z',' y+1/2',' -x'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z',' y+1/2',' x'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['y',' x+1/2',' -z'],
              ['-y',' -x+1/2',' -z'],
              ['-x',' z+1/2',' y'],
              ['-x',' -z+1/2',' -y'],
              ['z',' -y+1/2',' x'],
              ['-z',' -y+1/2',' -x'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['y',' -x+1/2',' -z'],
              ['x',' y+1/2',' -z+1/2'],
              ['-y',' x+1/2',' -z'],
              ['-x',' z+1/2',' -y'],
              ['-x',' y+1/2',' z+1/2'],
              ['-x',' -z+1/2',' y'],
              ['-z',' -y+1/2',' x'],
              ['x',' -y+1/2',' z+1/2'],
              ['z',' -y+1/2',' -x'],
              ['-z',' -x+1/2',' -y+1/2'],
              ['-y',' -z+1/2',' -x+1/2'],
              ['y',' z+1/2',' -x+1/2'],
              ['-z',' x+1/2',' y+1/2'],
              ['y',' -z+1/2',' x+1/2'],
              ['z',' x+1/2',' -y+1/2'],
              ['z',' -x+1/2',' y+1/2'],
              ['-y',' z+1/2',' x+1/2'],
              ['-y',' -x+1/2',' z'],
              ['y',' x+1/2',' z'],
              ['x',' -z+1/2',' -y'],
              ['x',' z+1/2',' y'],
              ['-z',' y+1/2',' -x'],
              ['z',' y+1/2',' x'],
              ['x+1/2',' y',' z+1/2'],
              ['-y+1/2',' x',' z'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y+1/2',' -x',' z'],
              ['x+1/2',' -z',' y'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x+1/2',' z',' -y'],
              ['z+1/2',' y',' -x'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z+1/2',' y',' x'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['y+1/2',' x',' -z'],
              ['-y+1/2',' -x',' -z'],
              ['-x+1/2',' z',' y'],
              ['-x+1/2',' -z',' -y'],
              ['z+1/2',' -y',' x'],
              ['-z+1/2',' -y',' -x'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['y+1/2',' -x',' -z'],
              ['x+1/2',' y',' -z+1/2'],
              ['-y+1/2',' x',' -z'],
              ['-x+1/2',' z',' -y'],
              ['-x+1/2',' y',' z+1/2'],
              ['-x+1/2',' -z',' y'],
              ['-z+1/2',' -y',' x'],
              ['x+1/2',' -y',' z+1/2'],
              ['z+1/2',' -y',' -x'],
              ['-z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' -z',' -x+1/2'],
              ['y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' x',' y+1/2'],
              ['y+1/2',' -z',' x+1/2'],
              ['z+1/2',' x',' -y+1/2'],
              ['z+1/2',' -x',' y+1/2'],
              ['-y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -x',' z'],
              ['y+1/2',' x',' z'],
              ['x+1/2',' -z',' -y'],
              ['x+1/2',' z',' y'],
              ['-z+1/2',' y',' -x'],
              ['z+1/2',' y',' x'],
              ['x+1/2',' y+1/2',' z'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' y+1/2'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x+1/2',' z+1/2',' -y+1/2'],
              ['z+1/2',' y+1/2',' -x+1/2'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-z+1/2',' y+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' y+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z+1/2',' -y+1/2',' x+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['-x+1/2',' y+1/2',' z'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['x+1/2',' -y+1/2',' z'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' -z+1/2',' -x'],
              ['y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' x+1/2',' y'],
              ['y+1/2',' -z+1/2',' x'],
              ['z+1/2',' x+1/2',' -y'],
              ['z+1/2',' -x+1/2',' y'],
              ['-y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    'F 4d 2 3 -1d' : [['x',' y',' z'],
              ['-x+1/4',' -y+1/4',' -z+1/4'],
              ['-y+1/4',' x+1/4',' z+1/4'],
              ['-x',' -y',' z'],
              ['y+1/4',' -x+1/4',' z+1/4'],
              ['x+1/4',' -z+1/4',' y+1/4'],
              ['x',' -y',' -z'],
              ['x+1/4',' z+1/4',' -y+1/4'],
              ['z+1/4',' y+1/4',' -x+1/4'],
              ['-x',' y',' -z'],
              ['-z+1/4',' y+1/4',' x+1/4'],
              ['y',' -x',' -z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['z',' -y',' -x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-z+1/4',' -x+1/4',' -y+1/4'],
              ['-y+1/4',' -z+1/4',' -x+1/4'],
              ['y+1/4',' z+1/4',' -x+1/4'],
              ['-z+1/4',' x+1/4',' y+1/4'],
              ['y+1/4',' -z+1/4',' x+1/4'],
              ['z+1/4',' x+1/4',' -y+1/4'],
              ['z+1/4',' -x+1/4',' y+1/4'],
              ['-y+1/4',' z+1/4',' x+1/4'],
              ['y+1/4',' x+1/4',' -z+1/4'],
              ['-y+1/4',' -x+1/4',' -z+1/4'],
              ['-x+1/4',' z+1/4',' y+1/4'],
              ['-x+1/4',' -z+1/4',' -y+1/4'],
              ['z+1/4',' -y+1/4',' x+1/4'],
              ['-z+1/4',' -y+1/4',' -x+1/4'],
              ['x+1/4',' y+1/4',' -z+1/4'],
              ['-x+1/4',' y+1/4',' z+1/4'],
              ['x+1/4',' -y+1/4',' z+1/4'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/4',' -y-1/4',' -z-1/4'],
              ['-y+1/4',' x-1/4',' z-1/4'],
              ['-x',' -y+1/2',' z+1/2'],
              ['y+1/4',' -x-1/4',' z-1/4'],
              ['x+1/4',' -z-1/4',' y-1/4'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x+1/4',' z-1/4',' -y-1/4'],
              ['z+1/4',' y-1/4',' -x-1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z+1/4',' y-1/4',' x-1/4'],
              ['y',' -x+1/2',' -z+1/2'],
              ['-y',' x+1/2',' -z+1/2'],
              ['-x',' z+1/2',' -y+1/2'],
              ['-x',' -z+1/2',' y+1/2'],
              ['-z',' -y+1/2',' x+1/2'],
              ['z',' -y+1/2',' -x+1/2'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-z+1/4',' -x-1/4',' -y-1/4'],
              ['-y+1/4',' -z-1/4',' -x-1/4'],
              ['y+1/4',' z-1/4',' -x-1/4'],
              ['-z+1/4',' x-1/4',' y-1/4'],
              ['y+1/4',' -z-1/4',' x-1/4'],
              ['z+1/4',' x-1/4',' -y-1/4'],
              ['z+1/4',' -x-1/4',' y-1/4'],
              ['-y+1/4',' z-1/4',' x-1/4'],
              ['y+1/4',' x-1/4',' -z-1/4'],
              ['-y+1/4',' -x-1/4',' -z-1/4'],
              ['-x+1/4',' z-1/4',' y-1/4'],
              ['-x+1/4',' -z-1/4',' -y-1/4'],
              ['z+1/4',' -y-1/4',' x-1/4'],
              ['-z+1/4',' -y-1/4',' -x-1/4'],
              ['x+1/4',' y-1/4',' -z-1/4'],
              ['-x+1/4',' y-1/4',' z-1/4'],
              ['x+1/4',' -y-1/4',' z-1/4'],
              ['-y',' -x+1/2',' z+1/2'],
              ['y',' x+1/2',' z+1/2'],
              ['x',' -z+1/2',' -y+1/2'],
              ['x',' z+1/2',' y+1/2'],
              ['-z',' y+1/2',' -x+1/2'],
              ['z',' y+1/2',' x+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-x-1/4',' -y+1/4',' -z-1/4'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x+1/4',' z-1/4'],
              ['x-1/4',' -z+1/4',' y-1/4'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x-1/4',' z+1/4',' -y-1/4'],
              ['z-1/4',' y+1/4',' -x-1/4'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z-1/4',' y+1/4',' x-1/4'],
              ['y+1/2',' -x',' -z+1/2'],
              ['-y+1/2',' x',' -z+1/2'],
              ['-x+1/2',' z',' -y+1/2'],
              ['-x+1/2',' -z',' y+1/2'],
              ['-z+1/2',' -y',' x+1/2'],
              ['z+1/2',' -y',' -x+1/2'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-z-1/4',' -x+1/4',' -y-1/4'],
              ['-y-1/4',' -z+1/4',' -x-1/4'],
              ['y-1/4',' z+1/4',' -x-1/4'],
              ['-z-1/4',' x+1/4',' y-1/4'],
              ['y-1/4',' -z+1/4',' x-1/4'],
              ['z-1/4',' x+1/4',' -y-1/4'],
              ['z-1/4',' -x+1/4',' y-1/4'],
              ['-y-1/4',' z+1/4',' x-1/4'],
              ['y-1/4',' x+1/4',' -z-1/4'],
              ['-y-1/4',' -x+1/4',' -z-1/4'],
              ['-x-1/4',' z+1/4',' y-1/4'],
              ['-x-1/4',' -z+1/4',' -y-1/4'],
              ['z-1/4',' -y+1/4',' x-1/4'],
              ['-z-1/4',' -y+1/4',' -x-1/4'],
              ['x-1/4',' y+1/4',' -z-1/4'],
              ['-x-1/4',' y+1/4',' z-1/4'],
              ['x-1/4',' -y+1/4',' z-1/4'],
              ['-y+1/2',' -x',' z+1/2'],
              ['y+1/2',' x',' z+1/2'],
              ['x+1/2',' -z',' -y+1/2'],
              ['x+1/2',' z',' y+1/2'],
              ['-z+1/2',' y',' -x+1/2'],
              ['z+1/2',' y',' x+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-x-1/4',' -y-1/4',' -z+1/4'],
              ['-y-1/4',' x-1/4',' z+1/4'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x-1/4',' -z-1/4',' y+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x-1/4',' z-1/4',' -y+1/4'],
              ['z-1/4',' y-1/4',' -x+1/4'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-z-1/4',' y-1/4',' x+1/4'],
              ['y+1/2',' -x+1/2',' -z'],
              ['-y+1/2',' x+1/2',' -z'],
              ['-x+1/2',' z+1/2',' -y'],
              ['-x+1/2',' -z+1/2',' y'],
              ['-z+1/2',' -y+1/2',' x'],
              ['z+1/2',' -y+1/2',' -x'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-z-1/4',' -x-1/4',' -y+1/4'],
              ['-y-1/4',' -z-1/4',' -x+1/4'],
              ['y-1/4',' z-1/4',' -x+1/4'],
              ['-z-1/4',' x-1/4',' y+1/4'],
              ['y-1/4',' -z-1/4',' x+1/4'],
              ['z-1/4',' x-1/4',' -y+1/4'],
              ['z-1/4',' -x-1/4',' y+1/4'],
              ['-y-1/4',' z-1/4',' x+1/4'],
              ['y-1/4',' x-1/4',' -z+1/4'],
              ['-y-1/4',' -x-1/4',' -z+1/4'],
              ['-x-1/4',' z-1/4',' y+1/4'],
              ['-x-1/4',' -z-1/4',' -y+1/4'],
              ['z-1/4',' -y-1/4',' x+1/4'],
              ['-z-1/4',' -y-1/4',' -x+1/4'],
              ['x-1/4',' y-1/4',' -z+1/4'],
              ['-x-1/4',' y-1/4',' z+1/4'],
              ['x-1/4',' -y-1/4',' z+1/4'],
              ['-y+1/2',' -x+1/2',' z'],
              ['y+1/2',' x+1/2',' z'],
              ['x+1/2',' -z+1/2',' -y'],
              ['x+1/2',' z+1/2',' y'],
              ['-z+1/2',' y+1/2',' -x'],
              ['z+1/2',' y+1/2',' x']],
    '-F 4vw 2vw 3' : [['x',' y',' z'],
              ['-y',' x+1/4',' z+1/4'],
              ['-x+1/4',' -y+1/4',' z'],
              ['y+1/4',' -x',' z+1/4'],
              ['x+1/4',' -z',' y+1/4'],
              ['x',' -y+1/4',' -z+1/4'],
              ['x+1/4',' z+1/4',' -y'],
              ['z+1/4',' y+1/4',' -x'],
              ['-x+1/4',' y',' -z+1/4'],
              ['-z',' y+1/4',' x+1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/4',' -z+1/4',' x'],
              ['z',' -x+1/4',' -y+1/4'],
              ['-y+1/4',' z',' -x+1/4'],
              ['-z+1/4',' -x+1/4',' y'],
              ['-z+1/4',' x',' -y+1/4'],
              ['y',' -z+1/4',' -x+1/4'],
              ['y+1/4',' x+1/4',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z+1/4',' y+1/4'],
              ['-x',' -z',' -y'],
              ['z+1/4',' -y',' x+1/4'],
              ['-z',' -y',' -x'],
              ['-x',' -y',' -z'],
              ['y',' -x-1/4',' -z-1/4'],
              ['x-1/4',' y-1/4',' -z'],
              ['-y-1/4',' x',' -z-1/4'],
              ['-x-1/4',' z',' -y-1/4'],
              ['-x',' y-1/4',' z-1/4'],
              ['-x-1/4',' -z-1/4',' y'],
              ['-z-1/4',' -y-1/4',' x'],
              ['x-1/4',' -y',' z-1/4'],
              ['z',' -y-1/4',' -x-1/4'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y-1/4',' z-1/4',' -x'],
              ['-z',' x-1/4',' y-1/4'],
              ['y-1/4',' -z',' x-1/4'],
              ['z-1/4',' x-1/4',' -y'],
              ['z-1/4',' -x',' y-1/4'],
              ['-y',' z-1/4',' x-1/4'],
              ['-y-1/4',' -x-1/4',' z'],
              ['y',' x',' z'],
              ['x',' -z-1/4',' -y-1/4'],
              ['x',' z',' y'],
              ['-z-1/4',' y',' -x-1/4'],
              ['z',' y',' x'],
              ['x',' y+1/2',' z+1/2'],
              ['-y',' x-1/4',' z-1/4'],
              ['-x+1/4',' -y-1/4',' z+1/2'],
              ['y+1/4',' -x+1/2',' z-1/4'],
              ['x+1/4',' -z+1/2',' y-1/4'],
              ['x',' -y-1/4',' -z-1/4'],
              ['x+1/4',' z-1/4',' -y+1/2'],
              ['z+1/4',' y-1/4',' -x+1/2'],
              ['-x+1/4',' y+1/2',' -z-1/4'],
              ['-z',' y-1/4',' x-1/4'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y+1/4',' -z-1/4',' x+1/2'],
              ['z',' -x-1/4',' -y-1/4'],
              ['-y+1/4',' z+1/2',' -x-1/4'],
              ['-z+1/4',' -x-1/4',' y+1/2'],
              ['-z+1/4',' x+1/2',' -y-1/4'],
              ['y',' -z-1/4',' -x-1/4'],
              ['y+1/4',' x-1/4',' -z+1/2'],
              ['-y',' -x+1/2',' -z+1/2'],
              ['-x',' z-1/4',' y-1/4'],
              ['-x',' -z+1/2',' -y+1/2'],
              ['z+1/4',' -y+1/2',' x-1/4'],
              ['-z',' -y+1/2',' -x+1/2'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['y',' -x+1/4',' -z+1/4'],
              ['x-1/4',' y+1/4',' -z+1/2'],
              ['-y-1/4',' x+1/2',' -z+1/4'],
              ['-x-1/4',' z+1/2',' -y+1/4'],
              ['-x',' y+1/4',' z+1/4'],
              ['-x-1/4',' -z+1/4',' y+1/2'],
              ['-z-1/4',' -y+1/4',' x+1/2'],
              ['x-1/4',' -y+1/2',' z+1/4'],
              ['z',' -y+1/4',' -x+1/4'],
              ['-z',' -x+1/2',' -y+1/2'],
              ['-y',' -z+1/2',' -x+1/2'],
              ['y-1/4',' z+1/4',' -x+1/2'],
              ['-z',' x+1/4',' y+1/4'],
              ['y-1/4',' -z+1/2',' x+1/4'],
              ['z-1/4',' x+1/4',' -y+1/2'],
              ['z-1/4',' -x+1/2',' y+1/4'],
              ['-y',' z+1/4',' x+1/4'],
              ['-y-1/4',' -x+1/4',' z+1/2'],
              ['y',' x+1/2',' z+1/2'],
              ['x',' -z+1/4',' -y+1/4'],
              ['x',' z+1/2',' y+1/2'],
              ['-z-1/4',' y+1/2',' -x+1/4'],
              ['z',' y+1/2',' x+1/2'],
              ['x+1/2',' y',' z+1/2'],
              ['-y+1/2',' x+1/4',' z-1/4'],
              ['-x-1/4',' -y+1/4',' z+1/2'],
              ['y-1/4',' -x',' z-1/4'],
              ['x-1/4',' -z',' y-1/4'],
              ['x+1/2',' -y+1/4',' -z-1/4'],
              ['x-1/4',' z+1/4',' -y+1/2'],
              ['z-1/4',' y+1/4',' -x+1/2'],
              ['-x-1/4',' y',' -z-1/4'],
              ['-z+1/2',' y+1/4',' x-1/4'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y-1/4',' -z+1/4',' x+1/2'],
              ['z+1/2',' -x+1/4',' -y-1/4'],
              ['-y-1/4',' z',' -x-1/4'],
              ['-z-1/4',' -x+1/4',' y+1/2'],
              ['-z-1/4',' x',' -y-1/4'],
              ['y+1/2',' -z+1/4',' -x-1/4'],
              ['y-1/4',' x+1/4',' -z+1/2'],
              ['-y+1/2',' -x',' -z+1/2'],
              ['-x+1/2',' z+1/4',' y-1/4'],
              ['-x+1/2',' -z',' -y+1/2'],
              ['z-1/4',' -y',' x-1/4'],
              ['-z+1/2',' -y',' -x+1/2'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['y+1/2',' -x-1/4',' -z+1/4'],
              ['x+1/4',' y-1/4',' -z+1/2'],
              ['-y+1/4',' x',' -z+1/4'],
              ['-x+1/4',' z',' -y+1/4'],
              ['-x+1/2',' y-1/4',' z+1/4'],
              ['-x+1/4',' -z-1/4',' y+1/2'],
              ['-z+1/4',' -y-1/4',' x+1/2'],
              ['x+1/4',' -y',' z+1/4'],
              ['z+1/2',' -y-1/4',' -x+1/4'],
              ['-z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' -z',' -x+1/2'],
              ['y+1/4',' z-1/4',' -x+1/2'],
              ['-z+1/2',' x-1/4',' y+1/4'],
              ['y+1/4',' -z',' x+1/4'],
              ['z+1/4',' x-1/4',' -y+1/2'],
              ['z+1/4',' -x',' y+1/4'],
              ['-y+1/2',' z-1/4',' x+1/4'],
              ['-y+1/4',' -x-1/4',' z+1/2'],
              ['y+1/2',' x',' z+1/2'],
              ['x+1/2',' -z-1/4',' -y+1/4'],
              ['x+1/2',' z',' y+1/2'],
              ['-z+1/4',' y',' -x+1/4'],
              ['z+1/2',' y',' x+1/2'],
              ['x+1/2',' y+1/2',' z'],
              ['-y+1/2',' x-1/4',' z+1/4'],
              ['-x-1/4',' -y-1/4',' z'],
              ['y-1/4',' -x+1/2',' z+1/4'],
              ['x-1/4',' -z+1/2',' y+1/4'],
              ['x+1/2',' -y-1/4',' -z+1/4'],
              ['x-1/4',' z-1/4',' -y'],
              ['z-1/4',' y-1/4',' -x'],
              ['-x-1/4',' y+1/2',' -z+1/4'],
              ['-z+1/2',' y-1/4',' x+1/4'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y-1/4',' -z-1/4',' x'],
              ['z+1/2',' -x-1/4',' -y+1/4'],
              ['-y-1/4',' z+1/2',' -x+1/4'],
              ['-z-1/4',' -x-1/4',' y'],
              ['-z-1/4',' x+1/2',' -y+1/4'],
              ['y+1/2',' -z-1/4',' -x+1/4'],
              ['y-1/4',' x-1/4',' -z'],
              ['-y+1/2',' -x+1/2',' -z'],
              ['-x+1/2',' z-1/4',' y+1/4'],
              ['-x+1/2',' -z+1/2',' -y'],
              ['z-1/4',' -y+1/2',' x+1/4'],
              ['-z+1/2',' -y+1/2',' -x'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['y+1/2',' -x+1/4',' -z-1/4'],
              ['x+1/4',' y+1/4',' -z'],
              ['-y+1/4',' x+1/2',' -z-1/4'],
              ['-x+1/4',' z+1/2',' -y-1/4'],
              ['-x+1/2',' y+1/4',' z-1/4'],
              ['-x+1/4',' -z+1/4',' y'],
              ['-z+1/4',' -y+1/4',' x'],
              ['x+1/4',' -y+1/2',' z-1/4'],
              ['z+1/2',' -y+1/4',' -x-1/4'],
              ['-z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' -z+1/2',' -x'],
              ['y+1/4',' z+1/4',' -x'],
              ['-z+1/2',' x+1/4',' y-1/4'],
              ['y+1/4',' -z+1/2',' x-1/4'],
              ['z+1/4',' x+1/4',' -y'],
              ['z+1/4',' -x+1/2',' y-1/4'],
              ['-y+1/2',' z+1/4',' x-1/4'],
              ['-y+1/4',' -x+1/4',' z'],
              ['y+1/2',' x+1/2',' z'],
              ['x+1/2',' -z+1/4',' -y-1/4'],
              ['x+1/2',' z+1/2',' y'],
              ['-z+1/4',' y+1/2',' -x-1/4'],
              ['z+1/2',' y+1/2',' x']],
    'F 4d 2 3 -1cd' : [['x',' y',' z'],
              ['-x+1/4',' -y+1/4',' -z-1/4'],
              ['-y+1/4',' x+1/4',' z+1/4'],
              ['-x',' -y',' z'],
              ['y+1/4',' -x+1/4',' z+1/4'],
              ['x+1/4',' -z+1/4',' y+1/4'],
              ['x',' -y',' -z'],
              ['x+1/4',' z+1/4',' -y+1/4'],
              ['z+1/4',' y+1/4',' -x+1/4'],
              ['-x',' y',' -z'],
              ['-z+1/4',' y+1/4',' x+1/4'],
              ['y',' -x',' -z+1/2'],
              ['-y',' x',' -z+1/2'],
              ['-x',' z',' -y+1/2'],
              ['-x',' -z',' y+1/2'],
              ['-z',' -y',' x+1/2'],
              ['z',' -y',' -x+1/2'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['-z+1/4',' -x+1/4',' -y-1/4'],
              ['-y+1/4',' -z+1/4',' -x-1/4'],
              ['y+1/4',' z+1/4',' -x-1/4'],
              ['-z+1/4',' x+1/4',' y-1/4'],
              ['y+1/4',' -z+1/4',' x-1/4'],
              ['z+1/4',' x+1/4',' -y-1/4'],
              ['z+1/4',' -x+1/4',' y-1/4'],
              ['-y+1/4',' z+1/4',' x-1/4'],
              ['y+1/4',' x+1/4',' -z+1/4'],
              ['-y+1/4',' -x+1/4',' -z+1/4'],
              ['-x+1/4',' z+1/4',' y+1/4'],
              ['-x+1/4',' -z+1/4',' -y+1/4'],
              ['z+1/4',' -y+1/4',' x+1/4'],
              ['-z+1/4',' -y+1/4',' -x+1/4'],
              ['x+1/4',' y+1/4',' -z-1/4'],
              ['-x+1/4',' y+1/4',' z-1/4'],
              ['x+1/4',' -y+1/4',' z-1/4'],
              ['-y',' -x',' z+1/2'],
              ['y',' x',' z+1/2'],
              ['x',' -z',' -y+1/2'],
              ['x',' z',' y+1/2'],
              ['-z',' y',' -x+1/2'],
              ['z',' y',' x+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-x+1/4',' -y-1/4',' -z+1/4'],
              ['-y+1/4',' x-1/4',' z-1/4'],
              ['-x',' -y+1/2',' z+1/2'],
              ['y+1/4',' -x-1/4',' z-1/4'],
              ['x+1/4',' -z-1/4',' y-1/4'],
              ['x',' -y+1/2',' -z+1/2'],
              ['x+1/4',' z-1/4',' -y-1/4'],
              ['z+1/4',' y-1/4',' -x-1/4'],
              ['-x',' y+1/2',' -z+1/2'],
              ['-z+1/4',' y-1/4',' x-1/4'],
              ['y',' -x+1/2',' -z'],
              ['-y',' x+1/2',' -z'],
              ['-x',' z+1/2',' -y'],
              ['-x',' -z+1/2',' y'],
              ['-z',' -y+1/2',' x'],
              ['z',' -y+1/2',' -x'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y',' -z+1/2',' x+1/2'],
              ['z',' -x+1/2',' -y+1/2'],
              ['-y',' z+1/2',' -x+1/2'],
              ['-z',' -x+1/2',' y+1/2'],
              ['-z',' x+1/2',' -y+1/2'],
              ['y',' -z+1/2',' -x+1/2'],
              ['-z+1/4',' -x-1/4',' -y+1/4'],
              ['-y+1/4',' -z-1/4',' -x+1/4'],
              ['y+1/4',' z-1/4',' -x+1/4'],
              ['-z+1/4',' x-1/4',' y+1/4'],
              ['y+1/4',' -z-1/4',' x+1/4'],
              ['z+1/4',' x-1/4',' -y+1/4'],
              ['z+1/4',' -x-1/4',' y+1/4'],
              ['-y+1/4',' z-1/4',' x+1/4'],
              ['y+1/4',' x-1/4',' -z-1/4'],
              ['-y+1/4',' -x-1/4',' -z-1/4'],
              ['-x+1/4',' z-1/4',' y-1/4'],
              ['-x+1/4',' -z-1/4',' -y-1/4'],
              ['z+1/4',' -y-1/4',' x-1/4'],
              ['-z+1/4',' -y-1/4',' -x-1/4'],
              ['x+1/4',' y-1/4',' -z+1/4'],
              ['-x+1/4',' y-1/4',' z+1/4'],
              ['x+1/4',' -y-1/4',' z+1/4'],
              ['-y',' -x+1/2',' z'],
              ['y',' x+1/2',' z'],
              ['x',' -z+1/2',' -y'],
              ['x',' z+1/2',' y'],
              ['-z',' y+1/2',' -x'],
              ['z',' y+1/2',' x'],
              ['x+1/2',' y',' z+1/2'],
              ['-x-1/4',' -y+1/4',' -z+1/4'],
              ['-y-1/4',' x+1/4',' z-1/4'],
              ['-x+1/2',' -y',' z+1/2'],
              ['y-1/4',' -x+1/4',' z-1/4'],
              ['x-1/4',' -z+1/4',' y-1/4'],
              ['x+1/2',' -y',' -z+1/2'],
              ['x-1/4',' z+1/4',' -y-1/4'],
              ['z-1/4',' y+1/4',' -x-1/4'],
              ['-x+1/2',' y',' -z+1/2'],
              ['-z-1/4',' y+1/4',' x-1/4'],
              ['y+1/2',' -x',' -z'],
              ['-y+1/2',' x',' -z'],
              ['-x+1/2',' z',' -y'],
              ['-x+1/2',' -z',' y'],
              ['-z+1/2',' -y',' x'],
              ['z+1/2',' -y',' -x'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y+1/2',' -z',' x+1/2'],
              ['z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' z',' -x+1/2'],
              ['-z+1/2',' -x',' y+1/2'],
              ['-z+1/2',' x',' -y+1/2'],
              ['y+1/2',' -z',' -x+1/2'],
              ['-z-1/4',' -x+1/4',' -y+1/4'],
              ['-y-1/4',' -z+1/4',' -x+1/4'],
              ['y-1/4',' z+1/4',' -x+1/4'],
              ['-z-1/4',' x+1/4',' y+1/4'],
              ['y-1/4',' -z+1/4',' x+1/4'],
              ['z-1/4',' x+1/4',' -y+1/4'],
              ['z-1/4',' -x+1/4',' y+1/4'],
              ['-y-1/4',' z+1/4',' x+1/4'],
              ['y-1/4',' x+1/4',' -z-1/4'],
              ['-y-1/4',' -x+1/4',' -z-1/4'],
              ['-x-1/4',' z+1/4',' y-1/4'],
              ['-x-1/4',' -z+1/4',' -y-1/4'],
              ['z-1/4',' -y+1/4',' x-1/4'],
              ['-z-1/4',' -y+1/4',' -x-1/4'],
              ['x-1/4',' y+1/4',' -z+1/4'],
              ['-x-1/4',' y+1/4',' z+1/4'],
              ['x-1/4',' -y+1/4',' z+1/4'],
              ['-y+1/2',' -x',' z'],
              ['y+1/2',' x',' z'],
              ['x+1/2',' -z',' -y'],
              ['x+1/2',' z',' y'],
              ['-z+1/2',' y',' -x'],
              ['z+1/2',' y',' x'],
              ['x+1/2',' y+1/2',' z'],
              ['-x-1/4',' -y-1/4',' -z-1/4'],
              ['-y-1/4',' x-1/4',' z+1/4'],
              ['-x+1/2',' -y+1/2',' z'],
              ['y-1/4',' -x-1/4',' z+1/4'],
              ['x-1/4',' -z-1/4',' y+1/4'],
              ['x+1/2',' -y+1/2',' -z'],
              ['x-1/4',' z-1/4',' -y+1/4'],
              ['z-1/4',' y-1/4',' -x+1/4'],
              ['-x+1/2',' y+1/2',' -z'],
              ['-z-1/4',' y-1/4',' x+1/4'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y+1/2',' -z+1/2',' x'],
              ['z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' z+1/2',' -x'],
              ['-z+1/2',' -x+1/2',' y'],
              ['-z+1/2',' x+1/2',' -y'],
              ['y+1/2',' -z+1/2',' -x'],
              ['-z-1/4',' -x-1/4',' -y-1/4'],
              ['-y-1/4',' -z-1/4',' -x-1/4'],
              ['y-1/4',' z-1/4',' -x-1/4'],
              ['-z-1/4',' x-1/4',' y-1/4'],
              ['y-1/4',' -z-1/4',' x-1/4'],
              ['z-1/4',' x-1/4',' -y-1/4'],
              ['z-1/4',' -x-1/4',' y-1/4'],
              ['-y-1/4',' z-1/4',' x-1/4'],
              ['y-1/4',' x-1/4',' -z+1/4'],
              ['-y-1/4',' -x-1/4',' -z+1/4'],
              ['-x-1/4',' z-1/4',' y+1/4'],
              ['-x-1/4',' -z-1/4',' -y+1/4'],
              ['z-1/4',' -y-1/4',' x+1/4'],
              ['-z-1/4',' -y-1/4',' -x+1/4'],
              ['x-1/4',' y-1/4',' -z-1/4'],
              ['-x-1/4',' y-1/4',' z-1/4'],
              ['x-1/4',' -y-1/4',' z-1/4'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    '-F 4cvw 2vw 3' : [['x',' y',' z'],
              ['-y',' x+1/4',' z-1/4'],
              ['-x+1/4',' -y+1/4',' z'],
              ['y+1/4',' -x',' z-1/4'],
              ['x+1/4',' -z',' y-1/4'],
              ['x',' -y+1/4',' -z+1/4'],
              ['x+1/4',' z-1/4',' -y'],
              ['z+1/4',' y-1/4',' -x'],
              ['-x+1/4',' y',' -z+1/4'],
              ['-z',' y+1/4',' x-1/4'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y+1/4',' -z+1/4',' x'],
              ['z',' -x+1/4',' -y+1/4'],
              ['-y+1/4',' z',' -x+1/4'],
              ['-z+1/4',' -x+1/4',' y'],
              ['-z+1/4',' x',' -y+1/4'],
              ['y',' -z+1/4',' -x+1/4'],
              ['y+1/4',' x-1/4',' -z'],
              ['-y',' -x',' -z+1/2'],
              ['-x',' z+1/4',' y-1/4'],
              ['-x',' -z',' -y+1/2'],
              ['z+1/4',' -y',' x-1/4'],
              ['-z',' -y',' -x+1/2'],
              ['-x',' -y',' -z'],
              ['y',' -x-1/4',' -z+1/4'],
              ['x-1/4',' y-1/4',' -z'],
              ['-y-1/4',' x',' -z+1/4'],
              ['-x-1/4',' z',' -y+1/4'],
              ['-x',' y-1/4',' z-1/4'],
              ['-x-1/4',' -z+1/4',' y'],
              ['-z-1/4',' -y+1/4',' x'],
              ['x-1/4',' -y',' z-1/4'],
              ['z',' -y-1/4',' -x+1/4'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y-1/4',' z-1/4',' -x'],
              ['-z',' x-1/4',' y-1/4'],
              ['y-1/4',' -z',' x-1/4'],
              ['z-1/4',' x-1/4',' -y'],
              ['z-1/4',' -x',' y-1/4'],
              ['-y',' z-1/4',' x-1/4'],
              ['-y-1/4',' -x+1/4',' z'],
              ['y',' x',' z+1/2'],
              ['x',' -z-1/4',' -y+1/4'],
              ['x',' z',' y+1/2'],
              ['-z-1/4',' y',' -x+1/4'],
              ['z',' y',' x+1/2'],
              ['x',' y+1/2',' z+1/2'],
              ['-y',' x-1/4',' z+1/4'],
              ['-x+1/4',' -y-1/4',' z+1/2'],
              ['y+1/4',' -x+1/2',' z+1/4'],
              ['x+1/4',' -z+1/2',' y+1/4'],
              ['x',' -y-1/4',' -z-1/4'],
              ['x+1/4',' z+1/4',' -y+1/2'],
              ['z+1/4',' y+1/4',' -x+1/2'],
              ['-x+1/4',' y+1/2',' -z-1/4'],
              ['-z',' y-1/4',' x+1/4'],
              ['z',' x+1/2',' y+1/2'],
              ['y',' z+1/2',' x+1/2'],
              ['-y+1/4',' -z-1/4',' x+1/2'],
              ['z',' -x-1/4',' -y-1/4'],
              ['-y+1/4',' z+1/2',' -x-1/4'],
              ['-z+1/4',' -x-1/4',' y+1/2'],
              ['-z+1/4',' x+1/2',' -y-1/4'],
              ['y',' -z-1/4',' -x-1/4'],
              ['y+1/4',' x+1/4',' -z+1/2'],
              ['-y',' -x+1/2',' -z'],
              ['-x',' z-1/4',' y+1/4'],
              ['-x',' -z+1/2',' -y'],
              ['z+1/4',' -y+1/2',' x+1/4'],
              ['-z',' -y+1/2',' -x'],
              ['-x',' -y+1/2',' -z+1/2'],
              ['y',' -x+1/4',' -z-1/4'],
              ['x-1/4',' y+1/4',' -z+1/2'],
              ['-y-1/4',' x+1/2',' -z-1/4'],
              ['-x-1/4',' z+1/2',' -y-1/4'],
              ['-x',' y+1/4',' z+1/4'],
              ['-x-1/4',' -z-1/4',' y+1/2'],
              ['-z-1/4',' -y-1/4',' x+1/2'],
              ['x-1/4',' -y+1/2',' z+1/4'],
              ['z',' -y+1/4',' -x-1/4'],
              ['-z',' -x+1/2',' -y+1/2'],
              ['-y',' -z+1/2',' -x+1/2'],
              ['y-1/4',' z+1/4',' -x+1/2'],
              ['-z',' x+1/4',' y+1/4'],
              ['y-1/4',' -z+1/2',' x+1/4'],
              ['z-1/4',' x+1/4',' -y+1/2'],
              ['z-1/4',' -x+1/2',' y+1/4'],
              ['-y',' z+1/4',' x+1/4'],
              ['-y-1/4',' -x-1/4',' z+1/2'],
              ['y',' x+1/2',' z'],
              ['x',' -z+1/4',' -y-1/4'],
              ['x',' z+1/2',' y'],
              ['-z-1/4',' y+1/2',' -x-1/4'],
              ['z',' y+1/2',' x'],
              ['x+1/2',' y',' z+1/2'],
              ['-y+1/2',' x+1/4',' z+1/4'],
              ['-x-1/4',' -y+1/4',' z+1/2'],
              ['y-1/4',' -x',' z+1/4'],
              ['x-1/4',' -z',' y+1/4'],
              ['x+1/2',' -y+1/4',' -z-1/4'],
              ['x-1/4',' z-1/4',' -y+1/2'],
              ['z-1/4',' y-1/4',' -x+1/2'],
              ['-x-1/4',' y',' -z-1/4'],
              ['-z+1/2',' y+1/4',' x+1/4'],
              ['z+1/2',' x',' y+1/2'],
              ['y+1/2',' z',' x+1/2'],
              ['-y-1/4',' -z+1/4',' x+1/2'],
              ['z+1/2',' -x+1/4',' -y-1/4'],
              ['-y-1/4',' z',' -x-1/4'],
              ['-z-1/4',' -x+1/4',' y+1/2'],
              ['-z-1/4',' x',' -y-1/4'],
              ['y+1/2',' -z+1/4',' -x-1/4'],
              ['y-1/4',' x-1/4',' -z+1/2'],
              ['-y+1/2',' -x',' -z'],
              ['-x+1/2',' z+1/4',' y+1/4'],
              ['-x+1/2',' -z',' -y'],
              ['z-1/4',' -y',' x+1/4'],
              ['-z+1/2',' -y',' -x'],
              ['-x+1/2',' -y',' -z+1/2'],
              ['y+1/2',' -x-1/4',' -z-1/4'],
              ['x+1/4',' y-1/4',' -z+1/2'],
              ['-y+1/4',' x',' -z-1/4'],
              ['-x+1/4',' z',' -y-1/4'],
              ['-x+1/2',' y-1/4',' z+1/4'],
              ['-x+1/4',' -z+1/4',' y+1/2'],
              ['-z+1/4',' -y+1/4',' x+1/2'],
              ['x+1/4',' -y',' z+1/4'],
              ['z+1/2',' -y-1/4',' -x-1/4'],
              ['-z+1/2',' -x',' -y+1/2'],
              ['-y+1/2',' -z',' -x+1/2'],
              ['y+1/4',' z-1/4',' -x+1/2'],
              ['-z+1/2',' x-1/4',' y+1/4'],
              ['y+1/4',' -z',' x+1/4'],
              ['z+1/4',' x-1/4',' -y+1/2'],
              ['z+1/4',' -x',' y+1/4'],
              ['-y+1/2',' z-1/4',' x+1/4'],
              ['-y+1/4',' -x+1/4',' z+1/2'],
              ['y+1/2',' x',' z'],
              ['x+1/2',' -z-1/4',' -y-1/4'],
              ['x+1/2',' z',' y'],
              ['-z+1/4',' y',' -x-1/4'],
              ['z+1/2',' y',' x'],
              ['x+1/2',' y+1/2',' z'],
              ['-y+1/2',' x-1/4',' z-1/4'],
              ['-x-1/4',' -y-1/4',' z'],
              ['y-1/4',' -x+1/2',' z-1/4'],
              ['x-1/4',' -z+1/2',' y-1/4'],
              ['x+1/2',' -y-1/4',' -z+1/4'],
              ['x-1/4',' z+1/4',' -y'],
              ['z-1/4',' y+1/4',' -x'],
              ['-x-1/4',' y+1/2',' -z+1/4'],
              ['-z+1/2',' y-1/4',' x-1/4'],
              ['z+1/2',' x+1/2',' y'],
              ['y+1/2',' z+1/2',' x'],
              ['-y-1/4',' -z-1/4',' x'],
              ['z+1/2',' -x-1/4',' -y+1/4'],
              ['-y-1/4',' z+1/2',' -x+1/4'],
              ['-z-1/4',' -x-1/4',' y'],
              ['-z-1/4',' x+1/2',' -y+1/4'],
              ['y+1/2',' -z-1/4',' -x+1/4'],
              ['y-1/4',' x+1/4',' -z'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z-1/4',' y-1/4'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z-1/4',' -y+1/2',' x-1/4'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['-x+1/2',' -y+1/2',' -z'],
              ['y+1/2',' -x+1/4',' -z+1/4'],
              ['x+1/4',' y+1/4',' -z'],
              ['-y+1/4',' x+1/2',' -z+1/4'],
              ['-x+1/4',' z+1/2',' -y+1/4'],
              ['-x+1/2',' y+1/4',' z-1/4'],
              ['-x+1/4',' -z-1/4',' y'],
              ['-z+1/4',' -y-1/4',' x'],
              ['x+1/4',' -y+1/2',' z-1/4'],
              ['z+1/2',' -y+1/4',' -x+1/4'],
              ['-z+1/2',' -x+1/2',' -y'],
              ['-y+1/2',' -z+1/2',' -x'],
              ['y+1/4',' z+1/4',' -x'],
              ['-z+1/2',' x+1/4',' y-1/4'],
              ['y+1/4',' -z+1/2',' x-1/4'],
              ['z+1/4',' x+1/4',' -y'],
              ['z+1/4',' -x+1/2',' y-1/4'],
              ['-y+1/2',' z+1/4',' x-1/4'],
              ['-y+1/4',' -x-1/4',' z'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/4',' -y+1/4'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/4',' y+1/2',' -x+1/4'],
              ['z+1/2',' y+1/2',' x+1/2']],
    # 229
    '-I 4 2 3' : [['x',' y',' z'],
              ['-y',' x',' z'],
              ['-x',' -y',' z'],
              ['y',' -x',' z'],
              ['x',' -z',' y'],
              ['x',' -y',' -z'],
              ['x',' z',' -y'],
              ['z',' y',' -x'],
              ['-x',' y',' -z'],
              ['-z',' y',' x'],
              ['z',' x',' y'],
              ['y',' z',' x'],
              ['-y',' -z',' x'],
              ['z',' -x',' -y'],
              ['-y',' z',' -x'],
              ['-z',' -x',' y'],
              ['-z',' x',' -y'],
              ['y',' -z',' -x'],
              ['y',' x',' -z'],
              ['-y',' -x',' -z'],
              ['-x',' z',' y'],
              ['-x',' -z',' -y'],
              ['z',' -y',' x'],
              ['-z',' -y',' -x'],
              ['-x',' -y',' -z'],
              ['y',' -x',' -z'],
              ['x',' y',' -z'],
              ['-y',' x',' -z'],
              ['-x',' z',' -y'],
              ['-x',' y',' z'],
              ['-x',' -z',' y'],
              ['-z',' -y',' x'],
              ['x',' -y',' z'],
              ['z',' -y',' -x'],
              ['-z',' -x',' -y'],
              ['-y',' -z',' -x'],
              ['y',' z',' -x'],
              ['-z',' x',' y'],
              ['y',' -z',' x'],
              ['z',' x',' -y'],
              ['z',' -x',' y'],
              ['-y',' z',' x'],
              ['-y',' -x',' z'],
              ['y',' x',' z'],
              ['x',' -z',' -y'],
              ['x',' z',' y'],
              ['-z',' y',' -x'],
              ['z',' y',' x'],
              ['x+1/2',' y+1/2',' z+1/2'],
              ['-y+1/2',' x+1/2',' z+1/2'],
              ['-x+1/2',' -y+1/2',' z+1/2'],
              ['y+1/2',' -x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' y+1/2'],
              ['x+1/2',' -y+1/2',' -z+1/2'],
              ['x+1/2',' z+1/2',' -y+1/2'],
              ['z+1/2',' y+1/2',' -x+1/2'],
              ['-x+1/2',' y+1/2',' -z+1/2'],
              ['-z+1/2',' y+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' y+1/2'],
              ['-z+1/2',' x+1/2',' -y+1/2'],
              ['y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' x+1/2',' -z+1/2'],
              ['-y+1/2',' -x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' y+1/2'],
              ['-x+1/2',' -z+1/2',' -y+1/2'],
              ['z+1/2',' -y+1/2',' x+1/2'],
              ['-z+1/2',' -y+1/2',' -x+1/2'],
              ['-x+1/2',' -y+1/2',' -z+1/2'],
              ['y+1/2',' -x+1/2',' -z+1/2'],
              ['x+1/2',' y+1/2',' -z+1/2'],
              ['-y+1/2',' x+1/2',' -z+1/2'],
              ['-x+1/2',' z+1/2',' -y+1/2'],
              ['-x+1/2',' y+1/2',' z+1/2'],
              ['-x+1/2',' -z+1/2',' y+1/2'],
              ['-z+1/2',' -y+1/2',' x+1/2'],
              ['x+1/2',' -y+1/2',' z+1/2'],
              ['z+1/2',' -y+1/2',' -x+1/2'],
              ['-z+1/2',' -x+1/2',' -y+1/2'],
              ['-y+1/2',' -z+1/2',' -x+1/2'],
              ['y+1/2',' z+1/2',' -x+1/2'],
              ['-z+1/2',' x+1/2',' y+1/2'],
              ['y+1/2',' -z+1/2',' x+1/2'],
              ['z+1/2',' x+1/2',' -y+1/2'],
              ['z+1/2',' -x+1/2',' y+1/2'],
              ['-y+1/2',' z+1/2',' x+1/2'],
              ['-y+1/2',' -x+1/2',' z+1/2'],
              ['y+1/2',' x+1/2',' z+1/2'],
              ['x+1/2',' -z+1/2',' -y+1/2'],
              ['x+1/2',' z+1/2',' y+1/2'],
              ['-z+1/2',' y+1/2',' -x+1/2'],
              ['z+1/2',' y+1/2',' x+1/2']],
    # 230
    '-I 4bd 2c 3' : [['x', 'y', 'z'],
                     ['-y+1/4', 'x-1/4', 'z+1/4'],
                     ['-x', '-y+1/2', 'z'],
                     ['y+1/4', '-x+1/4', 'z-1/4'],
                     ['x+1/4', '-z+1/4', 'y-1/4'],
                     ['x', '-y', '-z+1/2'],
                     ['x-1/4', 'z+1/4', '-y+1/4'],
                     ['z-1/4', 'y+1/4', '-x+1/4'],
                     ['-x+1/2', 'y', '-z'],
                     ['-z+1/4', 'y-1/4', 'x+1/4'],
                     ['z', 'x', 'y'],
                     ['y', 'z', 'x'],
                     ['-y', '-z+1/2', 'x'],
                     ['z', '-x', '-y+1/2'],
                     ['-y+1/2', 'z', '-x'],
                     ['-z', '-x+1/2', 'y'],
                     ['-z+1/2', 'x', '-y'],
                     ['y', '-z', '-x+1/2'],
                     ['y-1/4', 'x+1/4', '-z+1/4'],
                     ['-y+1/4', '-x+1/4', '-z+1/4'],
                     ['-x+1/4', 'z-1/4', 'y+1/4'],
                     ['-x+1/4', '-z+1/4', '-y+1/4'],
                     ['z+1/4', '-y+1/4', 'x-1/4'],
                     ['-z+1/4', '-y+1/4', '-x+1/4'],
                     ['-x', '-y', '-z'],
                     ['y-1/4', '-x+1/4', '-z-1/4'],
                     ['x', 'y+1/2', '-z'],
                     ['-y-1/4', 'x-1/4', '-z+1/4'],
                     ['-x-1/4', 'z-1/4', '-y+1/4'],
                     ['-x', 'y', 'z+1/2'],
                     ['-x+1/4', '-z-1/4', 'y-1/4'],
                     ['-z+1/4', '-y-1/4', 'x-1/4'],
                     ['x+1/2', '-y', 'z'],
                     ['z-1/4', '-y+1/4', '-x-1/4'],
                     ['-z', '-x', '-y'],
                     ['-y', '-z', '-x'],
                     ['y', 'z+1/2', '-x'],
                     ['-z', 'x', 'y+1/2'],
                     ['y+1/2', '-z', 'x'],
                     ['z', 'x+1/2', '-y'],
                     ['z+1/2', '-x', 'y'],
                     ['-y', 'z', 'x+1/2'],
                     ['-y+1/4', '-x-1/4', 'z-1/4'],
                     ['y-1/4', 'x-1/4', 'z-1/4'],
                     ['x-1/4', '-z+1/4', '-y-1/4'],
                     ['x-1/4', 'z-1/4', 'y-1/4'],
                     ['-z-1/4', 'y-1/4', '-x+1/4'],
                     ['z-1/4', 'y-1/4', 'x-1/4'],
                     ['x+1/2', 'y+1/2', 'z+1/2'],
                     ['-y-1/4', 'x+1/4', 'z-1/4'],
                     ['-x+1/2', '-y', 'z+1/2'],
                     ['y-1/4', '-x-1/4', 'z+1/4'],
                     ['x-1/4', '-z-1/4', 'y+1/4'],
                     ['x+1/2', '-y+1/2', '-z'],
                     ['x+1/4', 'z-1/4', '-y-1/4'],
                     ['z+1/4', 'y-1/4', '-x-1/4'],
                     ['-x', 'y+1/2', '-z+1/2'],
                     ['-z-1/4', 'y+1/4', 'x-1/4'],
                     ['z+1/2', 'x+1/2', 'y+1/2'],
                     ['y+1/2', 'z+1/2', 'x+1/2'],
                     ['-y+1/2', '-z', 'x+1/2'],
                     ['z+1/2', '-x+1/2', '-y'],
                     ['-y', 'z+1/2', '-x+1/2'],
                     ['-z+1/2', '-x', 'y+1/2'],
                     ['-z', 'x+1/2', '-y+1/2'],
                     ['y+1/2', '-z+1/2', '-x'],
                     ['y+1/4', 'x-1/4', '-z-1/4'],
                     ['-y-1/4', '-x-1/4', '-z-1/4'],
                     ['-x-1/4', 'z+1/4', 'y-1/4'],
                     ['-x-1/4', '-z-1/4', '-y-1/4'],
                     ['z-1/4', '-y-1/4', 'x+1/4'],
                     ['-z-1/4', '-y-1/4', '-x-1/4'],
                     ['-x+1/2', '-y+1/2', '-z+1/2'],
                     ['y+1/4', '-x-1/4', '-z+1/4'],
                     ['x+1/2', 'y', '-z+1/2'],
                     ['-y+1/4', 'x+1/4', '-z-1/4'],
                     ['-x+1/4', 'z+1/4', '-y-1/4'],
                     ['-x+1/2', 'y+1/2', 'z'],
                     ['-x-1/4', '-z+1/4', 'y+1/4'],
                     ['-z-1/4', '-y+1/4', 'x+1/4'],
                     ['x', '-y+1/2', 'z+1/2'],
                     ['z+1/4', '-y-1/4', '-x+1/4'],
                     ['-z+1/2', '-x+1/2', '-y+1/2'],
                     ['-y+1/2', '-z+1/2', '-x+1/2'],
                     ['y+1/2', 'z', '-x+1/2'],
                     ['-z+1/2', 'x+1/2', 'y'],
                     ['y', '-z+1/2', 'x+1/2'],
                     ['z+1/2', 'x', '-y+1/2'],
                     ['z', '-x+1/2', 'y+1/2'],
                     ['-y+1/2', 'z+1/2', 'x'],
                     ['-y-1/4', '-x+1/4', 'z+1/4'],
                     ['y+1/4', 'x+1/4', 'z+1/4'],
                     ['x+1/4', '-z-1/4', '-y+1/4'],
                     ['x+1/4', 'z+1/4', 'y+1/4'],
                     ['-z+1/4', 'y+1/4', '-x-1/4'],
                     ['z+1/4', 'y+1/4', 'x+1/4']],
    #######################
    # Non-standard settings
    # 1
    'A 1' : [['x','y','z'],
             ['x','y+1/2','z+1/2']],
    'B 1' : [['x','y','z'],
             ['x+1/2','y','z+1/2']],
    'C 1' : [['x','y','z'],
             ['x+1/2','y+1/2','z']],
    'I 1' : [['x','y','z'],
             ['x+1/2','y+1/2','z+1/2']],
    'F 1' : [['x','y','z'],
             ['x','y+1/2','z+1/2'],
             ['x+1/2','y','z+1/2'],
             ['x+1/2','y+1/2'+'z']],
    # 2
    '-A 1' : [['x','y','z'],
              ['x','y+1/2','z+1/2'],
              ['-x','-y','-z'],
              ['-x','-y+1/2','-z+1/2']],
    '-B 1' : [['x','y','z'],
              ['x+1/2','y','z+1/2'],
              ['-x','-y','-z'],
              ['-x+1/2','-y','-z+1/2']],
    '-C 1' : [['x','y','z'],
              ['x+1/2','y+1/2','z'],
             ['-x','-y','-z'],
             ['-x+1/2','-y+1/2','-z']],
    '-I 1' : [['x','y','z'],
             ['x+1/2','y+1/2','z+1/2'],
             ['-x','-y','-z'],
             ['-x+1/2','-y+1/2','-z+1/2']],
    '-F 1' : [['x','y','z'],
             ['x','y+1/2','z+1/2'],
             ['x+1/2','y','z+1/2'],
             ['x+1/2','y+1/2'+'z'],
             ['-x','-y','-z'],
             ['-x','-y+1/2','-z+1/2'],
             ['-x+1/2','-y','-z+1/2'],
             ['-x+1/2','-y+1/2'+'-z']],
    # 5
    'F 2' : [['x', 'y', 'z'],
             ['-x', '-y', 'z'],
             ['x', 'y+1/2', 'z+1/2'],
             ['-x', '-y+1/2', 'z+1/2'],
             ['x+1/2', 'y', 'z+1/2'],
             ['-x+1/2', '-y', 'z+1/2'],
             ['x+1/2', 'y+1/2', 'z'],
             ['-x+1/2', '-y+1/2', 'z']],
    'F 2x' : [['x', 'y', 'z'],
             ['x', '-y', '-z'],
             ['x', 'y+1/2', 'z+1/2'],
             ['x', '-y+1/2', '-z+1/2'],
             ['x+1/2', 'y', 'z+1/2'],
             ['x+1/2', '-y', '-z+1/2'],
             ['x+1/2', 'y+1/2', 'z'],
             ['x+1/2', '-y+1/2', '-z']],
    'F 2y' : [['x', 'y', 'z'],
             ['-x', 'y', '-z'],
             ['x', 'y+1/2', 'z+1/2'],
             ['-x', 'y+1/2', '-z+1/2'],
             ['x+1/2', 'y', 'z+1/2'],
             ['-x+1/2', 'y', '-z+1/2'],
             ['x+1/2', 'y+1/2', 'z'],
             ['-x+1/2', 'y+1/2', '-z']],
    # 7
    'B -2yc' : [['x', 'y', 'z'],
                ['x', '-y', 'z+1/2'],
                ['x+1/2', 'y', 'z+1/2'],
                ['x+1/2', '-y', 'z']],
    # 8
    'F -2' : [['x', 'y', 'z'],
               ['x', 'y', '-z'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x', 'y+1/2', '-z+1/2'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x+1/2', 'y', '-z+1/2'],
               ['x+1/2', 'y+1/2', 'z'],
               ['x+1/2', 'y+1/2', '-z']],
    'F -2x' : [['x', 'y', 'z'],
               ['-x', 'y', 'z'],
               ['x', 'y+1/2', 'z+1/2'],
               ['-x', 'y+1/2', 'z+1/2'],
               ['x+1/2', 'y', 'z+1/2'],
               ['-x+1/2', 'y', 'z+1/2'],
               ['x+1/2', 'y+1/2', 'z'],
               ['-x+1/2', 'y+1/2', 'z']],
    'F -2y' : [['x', 'y', 'z'],
               ['x', '-y', 'z'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x', '-y+1/2', 'z+1/2'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x+1/2', '-y', 'z+1/2'],
               ['x+1/2', 'y+1/2', 'z'],
               ['x+1/2', '-y+1/2', 'z']],
    # 9
    'F -2d' : [['x', 'y', 'z'],
               ['x+1/4', 'y+1/4', '-z+1/4'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x+1/4', 'y-1/4', '-z-1/4'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x-1/4', 'y+1/4', '-z-1/4'],
               ['x+1/2', 'y+1/2', 'z'],
               ['x-1/4', 'y-1/4', '-z+1/4']],
    'F -2xd' : [['x', 'y', 'z'],
               ['-x+1/4', 'y+1/4', 'z+1/4'],
               ['x', 'y+1/2', 'z+1/2'],
               ['-x+1/4', 'y-1/4', 'z-1/4'],
               ['x+1/2', 'y', 'z+1/2'],
               ['-x-1/4', 'y+1/4', 'z-1/4'],
               ['x+1/2', 'y+1/2', 'z'],
               ['-x-1/4', 'y-1/4', 'z+1/4']],
    'F -2yd' : [['x', 'y', 'z'],
               ['x+1/4', '-y+1/4', 'z+1/4'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x+1/4', '-y-1/4', 'z-1/4'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x-1/4', '-y+1/4', 'z-1/4'],
               ['x+1/2', 'y+1/2', 'z'],
               ['x-1/4', '-y-1/4', 'z+1/4']],
    # 12
    '-F 2' : [['x', 'y', 'z'],
               ['x', 'y', '-z'],
               ['-x', '-y', '-z'],
               ['-x', '-y', 'z'],
               ['x', 'y+1/2', '-z+1/2'],
               ['x+1/2', 'y', '-z+1/2'],
               ['x+1/2', 'y+1/2', '-z'],
               ['-x', '-y+1/2', '-z+1/2'],
               ['-x+1/2', '-y', '-z+1/2'],
               ['-x+1/2', '-y+1/2', '-z'],
               ['-x', '-y+1/2', 'z+1/2'],
               ['-x+1/2', '-y', 'z+1/2'],
               ['-x+1/2', '-y+1/2', 'z'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x+1/2', 'y+1/2', 'z']],
    '-F 2x' : [['x', 'y', 'z'],
               ['-x', 'y', 'z'],
               ['-x', '-y', '-z'],
               ['x', '-y', '-z'],
               ['-x', 'y+1/2', 'z+1/2'],
               ['-x+1/2', 'y', 'z+1/2'],
               ['-x+1/2', 'y+1/2', 'z'],
               ['-x', '-y+1/2', '-z+1/2'],
               ['-x+1/2', '-y', '-z+1/2'],
               ['-x+1/2', '-y+1/2', '-z'],
               ['x', '-y+1/2', '-z+1/2'],
               ['x+1/2', '-y', '-z+1/2'],
               ['x+1/2', '-y+1/2', '-z'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x+1/2', 'y+1/2', 'z']],
    '-F 2y' : [['x', 'y', 'z'],
               ['x', '-y', 'z'],
               ['-x', '-y', '-z'],
               ['-x', 'y', '-z'],
               ['x', '-y+1/2', 'z+1/2'],
               ['x+1/2', '-y', 'z+1/2'],
               ['x+1/2', '-y+1/2', 'z'],
               ['-x', '-y+1/2', '-z+1/2'],
               ['-x+1/2', '-y', '-z+1/2'],
               ['-x+1/2', '-y+1/2', '-z'],
               ['-x', 'y+1/2', '-z+1/2'],
               ['-x+1/2', 'y', '-z+1/2'],
               ['-x+1/2', 'y+1/2', '-z'],
               ['x', 'y+1/2', 'z+1/2'],
               ['x+1/2', 'y', 'z+1/2'],
               ['x+1/2', 'y+1/2', 'z']],
    # 15
    'F 2ycuw -1c' : [['x', 'y', 'z'],
                     ['-x', '-y', '-z+1/2'],
                     ['-x+1/4', 'y', '-z-1/4'],
                     ['x+1/4', '-y', 'z+1/4'],
                     ['x', 'y+1/2', 'z+1/2'],
                     ['-x', '-y+1/2', '-z'],
                     ['-x+1/4', 'y+1/2', '-z+1/4'],
                     ['x+1/4', '-y+1/2', 'z-1/4'],
                     ['x+1/2', 'y', 'z+1/2'],
                     ['-x+1/2', '-y', '-z'],
                     ['-x-1/4', 'y', '-z+1/4'],
                     ['x-1/4', '-y', 'z-1/4'],
                     ['x+1/2', 'y+1/2', 'z'],
                     ['-x+1/2', '-y+1/2', '-z+1/2'],
                     ['-x-1/4', 'y+1/2', '-z-1/4']],
    # 70
    '-F 2 2 -1d' : [['x', 'y', 'z'],
                    ['-x+1/4', '-y+1/4', 'z'],
                    ['x', '-y+1/4', '-z+1/4'],
                    ['-x+1/4', 'y', '-z+1/4'],
                    ['-x', '-y', '-z'],
                    ['x-1/4', 'y-1/4', '-z'],
                    ['-x', 'y-1/4', 'z-1/4'],
                    ['x-1/4', '-y', 'z-1/4'],
                    ['x', 'y+1/2', 'z+1/2'],
                    ['-x+1/4', '-y-1/4', 'z+1/2'],
                    ['x', '-y-1/4', '-z-1/4'],
                    ['-x+1/4', 'y+1/2', '-z-1/4'],
                    ['-x', '-y+1/2', '-z+1/2'],
                    ['x-1/4', 'y+1/4', '-z+1/2'],
                    ['-x', 'y+1/4', 'z+1/4'],
                    ['x-1/4', '-y+1/2', 'z+1/4'],
                    ['x+1/2', 'y', 'z+1/2'],
                    ['-x-1/4', '-y+1/4', 'z+1/2'],
                    ['x+1/2', '-y+1/4', '-z-1/4'],
                    ['-x-1/4', 'y', '-z-1/4'],
                    ['-x+1/2', '-y', '-z+1/2'],
                    ['x+1/4', 'y-1/4', '-z+1/2'],
                    ['-x+1/2', 'y-1/4', 'z+1/4'],
                    ['x+1/4', '-y', 'z+1/4'],
                    ['x+1/2', 'y+1/2', 'z'],
                    ['-x-1/4', '-y-1/4', 'z'],
                    ['x+1/2', '-y-1/4', '-z+1/4'],
                    ['-x-1/4', 'y+1/2', '-z+1/4'],
                    ['-x+1/2', '-y+1/2', '-z'],
                    ['x+1/4', 'y+1/4', '-z'],
                    ['-x+1/2', 'y+1/4', 'z-1/4'],
                    ['x+1/4', '-y+1/2', 'z-1/4']],
    '-F 2uv 2vw' : [['x', 'y', 'z'],
                    ['-x+1/4', '-y+1/4', '-z+1/4'],
                    ['-x', '-y', 'z'],
                    ['x', '-y', '-z'],
                    ['-x', 'y', '-z'],
                    ['x+1/4', 'y+1/4', '-z+1/4'],
                    ['-x+1/4', 'y+1/4', 'z+1/4'],
                    ['x+1/4', '-y+1/4', 'z+1/4'],
                    ['x', 'y+1/2', 'z+1/2'],
                    ['-x+1/4', '-y-1/4', '-z-1/4'],
                    ['-x', '-y+1/2', 'z+1/2'],
                    ['x', '-y+1/2', '-z+1/2'],
                    ['-x', 'y+1/2', '-z+1/2'],
                    ['x+1/4', 'y-1/4', '-z-1/4'],
                    ['-x+1/4', 'y-1/4', 'z-1/4'],
                    ['x+1/4', '-y-1/4', 'z-1/4'],
                    ['x+1/2', 'y', 'z+1/2'],
                    ['-x-1/4', '-y+1/4', '-z-1/4'],
                    ['-x+1/2', '-y', 'z+1/2'],
                    ['x+1/2', '-y', '-z+1/2'],
                    ['-x+1/2', 'y', '-z+1/2'],
                    ['x-1/4', 'y+1/4', '-z-1/4'],
                    ['-x-1/4', 'y+1/4', 'z-1/4'],
                    ['x-1/4', '-y+1/4', 'z-1/4'],
                    ['x+1/2', 'y+1/2', 'z'],
                    ['-x-1/4', '-y-1/4', '-z+1/4'],
                    ['-x+1/2', '-y+1/2', 'z'],
                    ['x+1/2', '-y+1/2', '-z'],
                    ['-x+1/2', 'y+1/2', '-z'],
                    ['x-1/4', 'y-1/4', '-z+1/4'],
                    ['-x-1/4', 'y-1/4', 'z+1/4'],
                    ['x-1/4', '-y-1/4', 'z+1/4']],
    # 139
    '-F 4 2' :    [['x', '-y', '-z'],
                   ['y', '-x', '-z'],
                   ['y', 'x', '-z'],
                   ['-x', '-y', '-z'],
                   ['-x', 'y', '-z'],
                   ['-y', 'x', '-z'],
                   ['-y', '-x', '-z'],
                   ['x', 'y', '-z'],
                   ['x', '-y', 'z'],
                   ['y', '-x', 'z'],
                   ['y', 'x', 'z'],
                   ['-x', '-y', 'z'],
                   ['-x', 'y', 'z'],
                   ['-y', 'x', 'z'],
                   ['-y', '-x', 'z'],
                   ['x', 'y', 'z'],
                   ['x', '-y+1/2', '-z+1/2'],
                   ['x+1/2', '-y', '-z+1/2'],
                   ['x+1/2', '-y+1/2', '-z'],
                   ['y', '-x+1/2', '-z+1/2'],
                   ['y+1/2', '-x', '-z+1/2'],
                   ['y+1/2', '-x+1/2', '-z'],
                   ['y', 'x+1/2', '-z+1/2'],
                   ['y+1/2', 'x', '-z+1/2'],
                   ['y+1/2', 'x+1/2', '-z'],
                   ['-x', '-y+1/2', '-z+1/2'],
                   ['-x+1/2', '-y', '-z+1/2'],
                   ['-x+1/2', '-y+1/2', '-z'],
                   ['-x', 'y+1/2', '-z+1/2'],
                   ['-x+1/2', 'y', '-z+1/2'],
                   ['-x+1/2', 'y+1/2', '-z'],
                   ['-y', 'x+1/2', '-z+1/2'],
                   ['-y+1/2', 'x', '-z+1/2'],
                   ['-y+1/2', 'x+1/2', '-z'],
                   ['-y', '-x+1/2', '-z+1/2'],
                   ['-y+1/2', '-x', '-z+1/2'],
                   ['-y+1/2', '-x+1/2', '-z'],
                   ['x', 'y+1/2', '-z+1/2'],
                   ['x+1/2', 'y', '-z+1/2'],
                   ['x+1/2', 'y+1/2', '-z'],
                   ['x', '-y+1/2', 'z+1/2'],
                   ['x+1/2', '-y', 'z+1/2'],
                   ['x+1/2', '-y+1/2', 'z'],
                   ['y', '-x+1/2', 'z+1/2'],
                   ['y+1/2', '-x', 'z+1/2'],
                   ['y+1/2', '-x+1/2', 'z'],
                   ['y', 'x+1/2', 'z+1/2'],
                   ['y+1/2', 'x', 'z+1/2'],
                   ['y+1/2', 'x+1/2', 'z'],
                   ['-x', '-y+1/2', 'z+1/2'],
                   ['-x+1/2', '-y', 'z+1/2'],
                   ['-x+1/2', '-y+1/2', 'z'],
                   ['-x', 'y+1/2', 'z+1/2'],
                   ['-x+1/2', 'y', 'z+1/2'],
                   ['-x+1/2', 'y+1/2', 'z'],
                   ['-y', 'x+1/2', 'z+1/2'],
                   ['-y+1/2', 'x', 'z+1/2'],
                   ['-y+1/2', 'x+1/2', 'z'],
                   ['-y', '-x+1/2', 'z+1/2'],
                   ['-y+1/2', '-x', 'z+1/2'],
                   ['-y+1/2', '-x+1/2', 'z'],
                   ['x', 'y+1/2', 'z+1/2'],
                   ['x+1/2', 'y', 'z+1/2'],
                   ['x+1/2', 'y+1/2', 'z']]
    }