1 1 1 P1 PG1 : sg no, no of lines, prim. ones SPGNAM PGNAM(IT volume A) X,Y,Z 2 1 1 P-1 PG1 X,Y,Z * -X,-Y,-Z 3 1 1 P2 PG2 X,Y,Z * -X,Y,-Z 4 1 1 P21 PG2 X,Y,Z * -X,1/2+Y,-Z 3004 2 1 I21 PG2 X,Y,Z * -X,1/2+Y,-Z X+1/2,Y+1/2,Z+1/2 * -X+1/2,Y,1/2-Z 1004 1 1 P1121 PG2 X,Y,Z * -X,-Y,1/2+Z 2005 2 1 A2 PG2 (Origin on screw along b) X, Y, Z * -X,1/2+Y,-Z X,1/2+Y,1/2+Z * -X, Y,1/2-Z 5 2 1 C2 PG2 X,Y,Z * -X,Y,-Z 1/2+X,1/2+Y,Z * 1/2-X,1/2+Y,-Z 1005 2 1 C21 PG2 (Origin on screw at 1/4X) X, Y, Z * -X,1/2+Y,-Z 1/2+X,1/2+Y,Z * 1/2-X, Y,-Z 10 1 1 P2/m PG2 X,Y,Z * X,-Y,Z * -X,Y,-Z * -X,-Y,-Z 12 2 1 C2/m PG2 X,Y,Z * X,-Y,Z * -X,Y,-Z * -X,-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 16 1 1 P222 PG222 X,Y,Z * -X,-Y,Z * X,-Y,-Z * -X,Y,-Z 17 1 1 P2221 PG222 standard version X,Y,Z * X,-Y,-Z * -X,-Y,1/2+Z * -X,Y,1/2-Z 1017 1 1 P2212 PG222 permuted version X,Y,Z * -X,-Y,Z * X,1/2-Y,-Z * -X,1/2+Y,-Z 18 1 1 P21212 PG222 standard version X,Y,Z * -X,-Y,Z * 1/2+X,1/2-Y,-Z * 1/2-X,1/2+Y,-Z 1018 1 1 P21212a PG222 origin on 21 21 ! shift (1/4,1/4,0) X,Y,Z * 1/2-X,1/2-Y,Z * X+1/2,-Y,-Z * -X,Y+1/2,-Z 19 1 1 P212121 PG222 X,Y,Z * 1/2-X,-Y,1/2+Z * 1/2+X,1/2-Y,-Z * -X,1/2+Y,1/2-Z 20 3 1 C2221 PG222 X,Y,Z * X,-Y,-Z * -X,-Y,1/2+Z * -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 * 1/2-X,1/2+Y,1/2-Z 1020 2 1 C2221a PG222 ! P212121 with C centring ! shift(1/4,0,0) X,Y,Z * 1/2-X,-Y,1/2+Z * 1/2+X,1/2-Y,-Z * -X,1/2+Y,1/2-Z 1/2+X,1/2+Y,Z * -X,1/2-Y,1/2+Z * X,-Y,-Z * 1/2-X,Y,1/2-Z 21 3 1 C222 PG222 X,Y,Z * -X,-Y,Z * X,-Y,-Z * -X,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 1021 2 1 C222a PG222 ! C21212a origin on 21 21 X,Y,Z * 1/2-X,1/2-Y,Z * X+1/2,-Y,-Z * -X,Y+1/2,-Z 1/2+ X,1/2+Y,Z * -X,-Y,Z * X,1/2-Y,-Z * 1/2-X,Y,-Z 22 4 1 F222 PG222 ! same as 18 with face centring X,Y,Z * -X,-Y,Z * 1/2+X,1/2-Y,-Z * 1/2-X,1/2+Y,-Z X,Y+1/2,Z+1/2 * -X,-Y+1/2,Z+1/2 * 1/2+X,-Y,-Z+1/2 * 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,+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,-Y,-Z * -X,Y,-Z 23 3 1 I222 PG222 ! same as 18 with origin shift (1/4,1/4,1/4) X,Y,Z * -X,-Y,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 1/2-X,1/2+Y,1/2-Z * 1/2+X,1/2-Y,1/2-Z 24 2 1 I212121 PG222 ! same as 19 with I centring X,Y,Z * 1/2-X,-Y,1/2+Z * 1/2+X,1/2-Y,-Z * -X,1/2+Y,1/2-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 47 2 2 Pmmm PG222 X,Y,Z * -X,-Y,Z * X,-Y,-Z * -X,Y,-Z -X,-Y,-Z * X,Y,-Z * -X,Y,Z * X,-Y,Z 65 6 2 Cmmm PG222 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 69 8 2 Fmmm PG222 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 71 6 2 Immm PG222 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 75 1 1 P4 PG4 X,Y,Z * -X,-Y,Z * -Y,X,Z * Y,-X,Z 76 1 1 P41 PG4 X,Y,Z * -X,-Y,1/2+Z * -Y,X,1/4+Z * Y,-X,3/4+Z 77 1 1 P42 PG4 X,Y,Z * -X,-Y,Z * -Y,X,1/2+Z * Y,-X,1/2+Z 78 1 1 P43 PG4 X,Y,Z * -X,-Y,1/2+Z * -Y,X,3/4+Z * Y,-X,1/4+Z 79 4 2 I4 PG4 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 -Y+1/2,X+1/2,Z+1/2 * Y+1/2,-X+1/2,Z+1/2 83 2 2 P4/m PG4 X,Y,Z * -X,-Y,Z * -Y,X,Z * Y,-X,Z -X,-Y,-Z * X,Y,-Z * Y,-X,-Z * -Y,X,-Z 87 6 2 I4/m PG4 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+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 * 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 89 4 4 P422 PG422 X, Y, Z * -X, -Y, Z -Y, X, Z * Y, -X, Z -X, Y, -Z * X, -Y, -Z Y, X, -Z * -Y, -X, -Z 90 4 4 P4212 PG422 X, Y, Z * -X, -Y, 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 Y, X, -Z * -Y, -X, -Z 91 4 4 P4122 PG422 X, Y, Z * -X, -Y, Z+1/2 -Y, X, Z+1/4 * Y, -X, Z+3/4 -X, Y, -Z * X, -Y, -Z+1/2 Y, X, -Z+3/4 * -Y, -X, -Z+1/4 92 4 4 P41212 PG422 X, Y, Z * -X, -Y, Z+1/2 -Y+1/2, X+1/2, Z+1/4 * Y+1/2, -X+1/2, Z+3/4 -X+1/2, Y+1/2, -Z+1/4 * X+1/2, -Y+1/2, -Z+3/4 Y, X, -Z * -Y, -X, -Z+1/2 93 4 4 P4222 PG422 X, Y, Z * -X, -Y, Z -Y, X, Z+1/2 * Y, -X, Z+1/2 -X, Y, -Z * X, -Y, -Z Y, X, -Z+1/2 * -Y, -X, -Z+1/2 94 4 4 P42212 PG422 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 Y, X, -Z * -Y, -X, -Z 1094 4 4 P42212a PG422 origin on 21 21 ie Shift 1/4,1/4,1/4 X,Y,Z * 1/2-X,1/2-Y,Z -Y,X+1/2,1/2+Z * Y+1/2,-X,1/2+Z -X,Y+1/2,-Z * X+1/2,-Y,-Z Y,X,1/2-Z * 1/2-Y,1/2-X,1/2-Z 95 4 4 P4322 PG422 X, Y, Z * -X, -Y, Z+1/2 -Y, X, Z+3/4 * Y, -X, Z+1/4 -X, Y, -Z * X, -Y, -Z+1/2 Y, X, -Z+1/4 * -Y, -X, -Z+3/4 96 4 4 P43212 PG422 X, Y, Z * -X, -Y, Z+1/2 -Y+1/2, X+1/2, Z+3/4 * Y+1/2, -X+1/2, Z+1/4 -X+1/2, Y+1/2, -Z+3/4 * X+1/2, -Y+1/2, -Z+1/4 Y, X, -Z * -Y, -X, -Z+1/2 97 8 4 I422 PG422 X, Y, Z * -X, -Y, Z -Y, X, Z * Y, -X, Z -X, Y, -Z * X, -Y, -Z Y, X, -Z * -Y, -X, -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+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 98 8 4 I4122 PG422 X, Y, Z * -X+1/2, -Y+1/2, Z+1/2 -Y, X+1/2, Z+1/4 * Y+1/2, -X, Z+3/4 -X+1/2, Y, -Z+3/4 * X, -Y+1/2, -Z+1/4 Y+1/2, X+1/2, -Z+1/2 * -Y, -X, -Z 1/2+X, 1/2+Y, 1/2+Z * -X, -Y, +Z 1/2-Y, +X, 3/4+Z * +Y, 1/2-X, 1/4+Z -X, 1/2+Y, 1/4-Z * 1/2+X, -Y, 3/4-Z +Y, +X, -Z * 1/2-Y, 1/2-X, 1/2-Z 123 4 4 P4/mmm PG422 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, Z * -Y, -X, Z * Y, X, Z 139 12 4 I4/mmm PG422 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, 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+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 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 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 -Y+1/2, -X+1/2, Z+1/2 * Y+1/2, X+1/2, Z+1/2 143 1 1 P3 PG3 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z 144 1 1 P31 PG3 X,Y,Z * -Y,X-Y,1/3+Z * Y-X,-X,2/3+Z 145 1 1 P32 PG3 X,Y,Z * -Y,X-Y,2/3+Z * Y-X,-X,1/3+Z 146 3 1 R3 PG3 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z 1/3+X,2/3+Y,2/3+Z * 1/3-Y,2/3+X-Y,2/3+Z * 1/3+Y-X,2/3-X,2/3+Z 2/3+X,1/3+Y,1/3+Z * 2/3-Y,1/3+X-Y,1/3+Z * 2/3+Y-X,1/3-X,1/3+Z 147 2 2 P-3 PG3 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z -X,-Y,-Z * Y,-X+Y,-Z * -Y+X,X,-Z 148 6 2 R-3 PG3 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z -X,-Y,-Z * Y,-X+Y,-Z * -Y+X,X,-Z 1/3+X,2/3+Y,2/3+Z * 1/3-Y,2/3+X-Y,2/3+Z * 1/3+Y-X,2/3-X,2/3+Z 1/3-X,2/3-Y,2/3-Z * 1/3+Y,2/3-X+Y,2/3-Z * 1/3-Y+X,2/3+X,2/3-Z 2/3+X,1/3+Y,1/3+Z * 2/3-Y,1/3+X-Y,1/3+Z * 2/3+Y-X,1/3-X,1/3+Z 2/3-X,1/3-Y,1/3-Z * 2/3+Y,1/3-X+Y,1/3-Z * 2/3-Y+X,1/3+X,1/3-Z 149 6 6 P312 PG312 X,Y,Z -Y,X-Y,Z Y-X,-X,Z -Y,-X,-Z X,-Y+X,-Z -X+Y,Y,-Z 150 6 6 P321 PG321 X,Y,Z -Y,X-Y,Z Y-X,-X,Z Y,X,-Z -X,Y-X,-Z X-Y,-Y,-Z 151 6 6 P3112 PG312 X,Y,Z -Y,X-Y,Z+1/3 Y-X,-X,Z+2/3 -Y,-X,-Z+2/3 X,-Y+X,-Z -X+Y,Y,-Z+1/3 152 6 6 P3121 PG321 X,Y,Z -Y,X-Y,Z+1/3 Y-X,-X,Z+2/3 Y,X,-Z -X,Y-X,-Z+1/3 X-Y,-Y,-Z+2/3 153 6 6 P3212 PG312 X,Y,Z -Y,X-Y,Z+2/3 Y-X,-X,Z+1/3 -Y,-X,-Z+1/3 X,-Y+X,-Z -X+Y,Y,-Z+2/3 154 6 6 P3221 PG321 X,Y,Z -Y,X-Y,Z+2/3 Y-X,-X,Z+1/3 Y,X,-Z -X,Y-X,-Z+2/3 X-Y,-Y,-Z+1/3 155 6 2 R32 PG321 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z Y,X,-Z * X-Y,-Y,-Z * -X,Y-X,-Z 2/3+X,1/3+Y,1/3+Z * 2/3-Y,1/3+X-Y,1/3+Z * 2/3+Y-X,1/3-X,1/3+Z 2/3+Y,1/3+X,1/3-Z * 2/3+X-Y,1/3-Y,1/3-Z * 2/3-X,1/3+Y-X,1/3-Z 1/3+X,2/3+Y,2/3+Z * 1/3-Y,2/3+X-Y,2/3+Z * 1/3+Y-X,2/3-X,2/3+Z 1/3+Y,2/3+X,2/3-Z * 1/3+X-Y,2/3-Y,2/3-Z * 1/3-X,2/3+Y-X,2/3-Z 162 4 4 P-31m PG312 X, Y, Z * -Y, X-Y, Z * Y-X,-X, Z -Y,-X,-Z * Y-X, Y,-Z * X, X-Y,-Z -X,-Y,-Z * Y,-X+Y,-Z * -Y+X, X,-Z Y, X, Z * X-Y,-Y, Z * -X, Y-X, Z 164 4 4 P-3m1 PG321 X, Y, Z * -Y, X-Y, Z * Y-X,-X, Z -X,-Y,-Z * Y,-X+Y,-Z * -Y+X, X,-Z Y, X,-Z * -X, Y-X,-Z * X-Y,-Y,-Z -Y,-X, Z * X,-Y+X, Z * -X+Y, Y, Z 166 12 4 R-3m PG321 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z -X,-Y,-Z * Y,-X+Y,-Z * -Y+X,X,-Z Y,X,-Z * X-Y,-Y,-Z * -X,Y-X,-Z -Y,-X,Z * -X+Y,Y,Z * X,-Y+X,Z 1/3+X,2/3+Y,2/3+Z * 1/3-Y,2/3+X-Y,2/3+Z * 1/3+Y-X,2/3-X,2/3+Z 1/3-X,2/3-Y,2/3-Z * 1/3+Y,2/3-X+Y,2/3-Z * 1/3-Y+X,2/3+X,2/3-Z 1/3+Y,2/3+X,2/3-Z * 1/3+X-Y,2/3-Y,2/3-Z * 1/3-X,2/3+Y-X,2/3-Z 1/3-Y,2/3-X,2/3+Z * 1/3-X+Y,2/3+Y,2/3+Z * 1/3+X,2/3-Y+X,2/3+Z 2/3+X,1/3+Y,1/3+Z * 2/3-Y,1/3+X-Y,1/3+Z * 2/3+Y-X,1/3-X,1/3+Z 2/3-X,1/3-Y,1/3-Z * 2/3+Y,1/3-X+Y,1/3-Z * 2/3-Y+X,1/3+X,1/3-Z 2/3+Y,1/3+X,1/3-Z * 2/3+X-Y,1/3-Y,1/3-Z * 2/3-X,1/3+Y-X,1/3-Z 2/3-Y,1/3-X,1/3+Z * 2/3-X+Y,1/3+Y,1/3+Z * 2/3+X,1/3-Y+X,1/3+Z 168 1 1 P6 PG6 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z * -X,-Y,Z * Y,Y-X,Z * X-Y,X,Z 169 1 1 P61 PG6 X,Y,Z * -Y,X-Y,1/3+Z * Y-X,-X,2/3+Z * -X,-Y,1/2+Z * Y,Y-X,5/6+Z * X-Y,X,1/6+Z 170 1 1 P65 PG6 X,Y,Z * -Y,X-Y,2/3+Z * Y-X,-X,1/3+Z * -X,-Y,1/2+Z * Y,Y-X,1/6+Z * X-Y,X,5/6+Z 175 4 4 P6/m PG6 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z -X,-Y,Z * Y,Y-X,Z * X-Y,X,Z -X,-Y,-Z * Y,-X+Y,-Z * -Y+X,X,-Z X,Y,-Z * -Y,-Y+X,-Z * -X+Y,-X,-Z 177 4 4 P622 PG622 Note all 622 spacegroups in IT Vol 1 order (not Vol A) X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z -X,-Y,Z * Y,Y-X,Z * X-Y,X,Z Y,X,-Z * -X,Y-X,-Z * X-Y,-Y,-Z -Y,-X,-Z * X,X-Y,-Z * Y-X,Y,-Z 178 4 4 P6122 PG622 X,Y,Z * -Y,X-Y,1/3+Z * Y-X,-X,2/3+Z -X,-Y,1/2+Z * Y,Y-X,5/6+Z * X-Y, X,1/6+Z Y, X,1/3-Z * -X,Y-X,2/3-Z * X-Y,-Y,-Z -Y,-X,5/6-Z * X,X-Y,1/6-Z * Y-X, Y,1/2-Z 179 4 4 P6522 PG622 X,Y,Z * -Y,X-Y,2/3+Z * Y-X,-X,1/3+Z -X,-Y,1/2+Z * Y,Y-X,1/6+Z * X-Y, X,5/6+Z Y, X,2/3-Z * -X,Y-X,1/3-Z * X-Y,-Y,-Z -Y,-X,1/6-Z * X,X-Y,5/6-Z * Y-X, Y,1/2-Z 180 4 4 P6222 PG622 X,Y,Z * -Y,X-Y,2/3+Z * Y-X,-X,1/3+Z -X,-Y, Z * Y,Y-X,2/3+Z * X-Y, X,1/3+Z Y, X,2/3-Z * -X,Y-X,1/3-Z * X-Y,-Y,-Z -Y,-X,2/3-Z * X,X-Y,1/3-Z * Y-X, Y,-Z 181 4 4 P6422 PG622 X,Y,Z * -Y,X-Y,1/3+Z * Y-X,-X,2/3+Z -X,-Y, Z * Y,Y-X,1/3+Z * X-Y, X,2/3+Z Y, X,1/3-Z * -X,Y-X,2/3-Z * X-Y,-Y,-Z -Y,-X,1/3-Z * X,X-Y,2/3-Z * Y-X, Y,-Z 182 4 4 P6322 PG622 X,Y,Z * -Y,X-Y,Z * Y-X,-X,Z -X,-Y,Z+1/2 * Y,Y-X,Z+1/2 * X-Y,X,Z+1/2 Y,X,-Z * -X,Y-X,-Z * X-Y,-Y,-Z -Y,-X,-Z+1/2 * X,X-Y,-Z+1/2 * Y-X,Y,-Z+1/2 191 4 4 P6/mmm PG622 X, Y, Z * -Y,X-Y, Z * Y-X,-X, Z * Y, X, Z * -X,Y-X, Z * X-Y,-Y, Z -X,-Y, Z * Y,Y-X, Z * X-Y, X, Z * -Y,-X, Z * X,X-Y, Z * Y-X, Y, Z X, Y,-Z * -Y,X-Y,-Z * Y-X,-X,-Z * Y, X,-Z * -X,Y-X,-Z * X-Y,-Y,-Z -X,-Y,-Z * Y,Y-X,-Z * X-Y, X,-Z * -Y,-X,-Z * X,X-Y,-Z * Y-X, Y,-Z 195 3 3 P23 PG23 X, Y, Z * -X, -Y, +Z * -X, Y, -Z * +X, -Y, -Z Z, X, Y * +Z, -X, -Y * -Z, -X, +Y * -Z, +X, -Y Y, Z, X * -Y, +Z, -X * +Y, -Z, -X * -Y, -Z, +X 196 12 3 F23 PG23 +X, +Y, +Z * -X, -Y, +Z * -X, +Y, -Z * +X, -Y, -Z +Z, +X, +Y * +Z, -X, -Y * -Z, -X, +Y * -Z, +X, -Y +Y, +Z, +X * -Y, +Z, -X * +Y, -Z, -X * -Y, -Z, +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 * +Z, 1/2-X, 1/2-Y * -Z, 1/2-X, 1/2+Y * -Z, 1/2+X, 1/2-Y +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+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+Z, -X, 1/2-Y * 1/2-Z, -X, 1/2+Y * 1/2-Z, +X, 1/2-Y 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+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+Z, 1/2-X, -Y * 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+Z, -X * 1/2+Y, 1/2-Z, -X * 1/2-Y, 1/2-Z, +X 197 9 3 I23 PG23 +X, +Y, +Z * -X, -Y, +Z * -X, +Y, -Z * +X, -Y, -Z +Z, +X, +Y * +Z, -X, -Y * -Z, -X, +Y * -Z, +X, -Y +Y, +Z, +X * -Y, +Z, -X * +Y, -Z, -X * -Y, -Z, +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+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+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 198 6 6 P213 PG23 X, Y, Z * 1/2-X, -Y, 1/2+Z -X, 1/2+Y, 1/2-Z * 1/2+X, 1/2-Y, -Z Z, X, Y * 1/2+Z, 1/2-X, -Y 1/2-Z, -X, 1/2+Y * -Z, 1/2+X, 1/2-Y Y, Z, X * -Y, 1/2+Z, 1/2-X 1/2+Y, 1/2-Z, -X * 1/2-Y, -Z, 1/2+X 199 12 6 I213 PG23 X, Y, Z * 1/2-X, -Y, 1/2+Z -X, 1/2+Y, 1/2-Z * 1/2+X, 1/2-Y, -Z Z, X, Y * 1/2+Z, 1/2-X, -Y 1/2-Z, -X, 1/2+Y * -Z, 1/2+X, 1/2-Y 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+X, 1/2+Y, 1/2+Z * -X, 1/2-Y, +Z 1/2-X, +Y, -Z * +X, -Y, 1/2-Z 1/2+Z, 1/2+X, 1/2+Y * +Z, -X, 1/2-Y -Z, 1/2-X, +Y * 1/2-Z, +X, -Y 1/2+Y, 1/2+Z, 1/2+X * 1/2-Y, +Z, -X +Y, -Z, 1/2-X * -Y, 1/2-Z, +X 200 6 6 Pm-3 PG23 +X,+Y,+Z * -X,-Y,+Z * -X,+Y,-Z * +X,-Y,-Z +Z,+X,+Y * +Z,-X,-Y * -Z,-X,+Y * -Z,+X,-Y +Y,+Z,+X * -Y,+Z,-X * +Y,-Z,-X * -Y,-Z,+X +X,+Y,-Z * -X,-Y,-Z * +X,-Y,+Z * -X,+Y,+Z -Z,-X,-Y * -Z,+X,+Y * +Z,+X,-Y * +Z,-X,+Y -Y,-Z,-X * +Y,-Z,+X * -Y,+Z,+X * +Y,+Z,-X 202 24 6 Fm-3 PG23 +X,+Y,+Z * -X,-Y,+Z * -X,+Y,-Z * +X,-Y,-Z +Z,+X,+Y * +Z,-X,-Y * -Z,-X,+Y * -Z,+X,-Y +Y,+Z,+X * -Y,+Z,-X * +Y,-Z,-X * -Y,-Z,+X +X,+Y,-Z * -X,-Y,-Z * +X,-Y,+Z * -X,+Y,+Z -Z,-X,-Y * -Z,+X,+Y * +Z,+X,-Y * +Z,-X,+Y -Y,-Z,-X * +Y,-Z,+X * -Y,+Z,+X * +Y,+Z,-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 * +Z,1/2-X,1/2-Y * -Z,1/2-X,1/2+Y * -Z,1/2+X,1/2-Y +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 +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 * -Z,1/2+X,1/2+Y * +Z,1/2+X,1/2-Y * +Z,1/2-X,1/2+Y -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+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+Z,-X,1/2-Y * 1/2-Z,-X,1/2+Y * 1/2-Z,+X,1/2-Y 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+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-Z,+X,1/2+Y * 1/2+Z,+X,1/2-Y * 1/2+Z,-X,1/2+Y 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+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+Z,1/2-X,-Y * 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+Z,-X * 1/2+Y,1/2-Z,-X * 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-Z,1/2+X,+Y * 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-Z,+X * 1/2-Y,1/2+Z,+X * 1/2+Y,1/2+Z,-X 204 18 6 Im-3 PG23 +X,+Y,+Z * -X,-Y,+Z * -X,+Y,-Z * +X,-Y,-Z +Z,+X,+Y * +Z,-X,-Y * -Z,-X,+Y * -Z,+X,-Y +Y,+Z,+X * -Y,+Z,-X * +Y,-Z,-X * -Y,-Z,+X +X,+Y,-Z * -X,-Y,-Z * +X,-Y,+Z * -X,+Y,+Z -Z,-X,-Y * -Z,+X,+Y * +Z,+X,-Y * +Z,-X,+Y -Y,-Z,-X * +Y,-Z,+X * -Y,+Z,+X * +Y,+Z,-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+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+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+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-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-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 207 6 6 P432 PG432 +X, +Y, +Z * -X, -Y, +Z * -X, +Y, -Z * +X, -Y, -Z +Z, +X, +Y * +Z, -X, -Y * -Z, -X, +Y * -Z, +X, -Y +Y, +Z, +X * -Y, +Z, -X * +Y, -Z, -X * -Y, -Z, +X +Y, +X, -Z * -Y, -X, -Z * +Y, -X, +Z * -Y, +X, +Z +X, +Z, -Y * -X, +Z, +Y * -X, -Z, -Y * +X, -Z, +Y +Z, +Y, -X * +Z, -Y, +X * -Z, +Y, +X * -Z, -Y, -X 209 24 6 F432 PG432 +X, +Y, +Z * -X, -Y, +Z * -X, +Y, -Z * +X, -Y, -Z +Z, +X, +Y * +Z, -X, -Y * -Z, -X, +Y * -Z, +X, -Y +Y, +Z, +X * -Y, +Z, -X * +Y, -Z, -X * -Y, -Z, +X +Y, +X, -Z * -Y, -X, -Z * +Y, -X, +Z * -Y, +X, +Z +X, +Z, -Y * -X, +Z, +Y * -X, -Z, -Y * +X, -Z, +Y +Z, +Y, -X * +Z, -Y, +X * -Z, +Y, +X * -Z, -Y, -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 * +Z, 1/2-X, 1/2-Y * -Z, 1/2-X, 1/2+Y * -Z, 1/2+X, 1/2-Y +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+X, 1/2-Z * -Y, 1/2-X, 1/2-Z * +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 * -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+Y, 1/2+X * -Z, 1/2-Y, 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+Z, -X, 1/2-Y * 1/2-Z, -X, 1/2+Y * 1/2-Z, +X, 1/2-Y 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, +X, 1/2-Z * 1/2-Y, -X, 1/2-Z * 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-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, +Y, 1/2+X * 1/2-Z, -Y, 1/2-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+Z, 1/2-X, -Y * 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+Z, -X * 1/2+Y, 1/2-Z, -X * 1/2-Y, 1/2-Z, +X 1/2+Y, 1/2+X, -Z * 1/2-Y, 1/2-X, -Z * 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-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+Y, +X * 1/2-Z, 1/2-Y, -X 211 24 12 I432 PG432 X, Y, Z * -X, -Y, Z -X, Y, -Z * X, -Y, -Z Z, X, Y * Z, -X, -Y -Z, -X, Y * -Z, X, -Y Y, Z, X * -Y, Z, -X Y, -Z, -X * -Y, -Z, X Y, X, -Z * -Y, -X, -Z Y, -X, Z * -Y, X, Z X, Z, -Y * -X, Z, Y -X, -Z, -Y * X, -Z, Y Z, Y, -X * Z, -Y, X -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 * X+1/2,-Y+1/2, -Z+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 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, X+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, 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, 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,-Y+1/2, -X+1/2 214 24 12 I4132 PG432 X, Y, Z * -X+1/2, -Y, Z+1/2 -X, Y+1/2, -Z+1/2 * X+1/2, -Y+1/2, -Z Z, X, Y * Z+1/2, -X+1/2, -Y -Z+1/2, -X, Y+1/2 * -Z, X+1/2, -Y+1/2 Y, Z, X * -Y, Z+1/2, -X+1/2 Y+1/2, -Z+1/2, -X * -Y+1/2, -Z, X+1/2 Y+3/4, X+1/4, -Z+1/4 * -Y+3/4, -X+3/4, -Z+3/4 Y+1/4, -X+1/4, Z+3/4 * -Y+1/4, X+3/4, Z+1/4 X+3/4, Z+1/4, -Y+1/4 * -X+1/4, Z+3/4, Y+1/4 -X+3/4, -Z+3/4, -Y+3/4 * X+1/4, -Z+1/4, Y+3/4 Z+3/4, Y+1/4, -X+1/4 * Z+1/4, -Y+1/4, X+3/4 -Z+1/4, Y+3/4, X+1/4 * -Z+3/4, -Y+3/4, -X+3/4 X+1/2, Y+1/2, Z+1/2 * -X, -Y+1/2, Z -X+1/2, Y, -Z * X, -Y, -Z+1/2 Z+1/2, X+1/2, Y+1/2 * Z, -X, -Y+1/2 -Z, -X+1/2, Y * -Z+1/2, X, -Y 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+1/4, X+3/4, -Z+3/4 * -Y+1/4, -X+1/4, -Z+1/4 Y+3/4, -X+3/4, Z+1/4 * -Y+3/4, X+1/4, Z+3/4 X+1/4, Z+3/4, -Y+3/4 * -X+3/4, Z+1/4, Y+3/4 -X+1/4, -Z+1/4, -Y+1/4 * X+3/4, -Z+3/4, Y+1/4 Z+1/4, Y+3/4, -X+3/4 * Z+3/4, -Y+3/4, X+1/4 -Z+3/4, Y+1/4, X+3/4 * -Z+1/4, -Y+1/4, -X+1/4 221 24 24 Pm-3m PG432 X, Y, Z * -X, -Y, Z -X, Y, -Z * X, -Y, -Z Z, X, Y * Z, -X, -Y -Z, -X, Y * -Z, X, -Y Y, Z, X * -Y, Z, -X Y, -Z, -X * -Y, -Z, X Y, X, -Z * -Y, -X, -Z Y, -X, Z * -Y, X, Z X, Z, -Y * -X, Z, Y -X, -Z, -Y * X, -Z, Y Z, Y, -X * Z, -Y, X -Z, Y, X * -Z, -Y, -X -X, -Y, -Z * X, Y, -Z X, -Y, Z * -X, Y, Z -Z, -X, -Y * -Z, X, Y Z, X, -Y * Z, -X, Y -Y, -Z, -X * Y, -Z, X -Y, Z, X * Y, Z, -X -Y, -X, Z * Y, X, Z -Y, X, -Z * Y, -X, -Z -X, -Z, Y * X, -Z, -Y X, Z, Y * -X, Z, -Y -Z, -Y, X * -Z, Y, -X Z, -Y, -X * Z, Y, X 225 48 12 Fm-3m PG432 +X, +Y, +Z * -X, -Y, +Z * -X, +Y, -Z * +X, -Y, -Z +Z, +X, +Y * +Z, -X, -Y * -Z, -X, +Y * -Z, +X, -Y +Y, +Z, +X * -Y, +Z, -X * +Y, -Z, -X * -Y, -Z, +X +Y, +X, -Z * -Y, -X, -Z * +Y, -X, +Z * -Y, +X, +Z +X, +Z, -Y * -X, +Z, +Y * -X, -Z, -Y * +X, -Z, +Y +Z, +Y, -X * +Z, -Y, +X * -Z, +Y, +X * -Z, -Y, -X -X, -Y, -Z * +X, +Y, -Z * +X, -Y, +Z * -X, +Y, +Z -Z, -X, -Y * -Z, +X, +Y * +Z, +X, -Y * +Z, -X, +Y -Y, -Z, -X * +Y, -Z, +X * -Y, +Z, +X * +Y, +Z, -X -Y, -X, +Z * +Y, +X, +Z * -Y, +X, -Z * +Y, -X, -Z -X, -Z, +Y * +X, -Z, -Y * +X, +Z, +Y * -X, +Z, -Y -Z, -Y, +X * -Z, +Y, -X * +Z, -Y, -X * +Z, +Y, +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 * +Z, 1/2-X, 1/2-Y * -Z, 1/2-X, 1/2+Y * -Z, 1/2+X, 1/2-Y +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+X, 1/2-Z * -Y, 1/2-X, 1/2-Z * +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 * -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+Y, 1/2+X * -Z, 1/2-Y, 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 * -Z, 1/2+X, 1/2+Y * +Z, 1/2+X, 1/2-Y * +Z, 1/2-X, 1/2+Y -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-X, 1/2+Z * +Y, 1/2+X, 1/2+Z * -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 * +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-Y, 1/2-X * +Z, 1/2+Y, 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+Z, -X, 1/2-Y * 1/2-Z, -X, 1/2+Y * 1/2-Z, +X, 1/2-Y 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, +X, 1/2-Z * 1/2-Y, -X, 1/2-Z * 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-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, +Y, 1/2+X * 1/2-Z, -Y, 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-Z, +X, 1/2+Y * 1/2+Z, +X, 1/2-Y * 1/2+Z, -X, 1/2+Y 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, -X, 1/2+Z * 1/2+Y, +X, 1/2+Z * 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+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, -Y, 1/2-X * 1/2+Z, +Y, 1/2+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+Z, 1/2-X, -Y * 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+Z, -X * 1/2+Y, 1/2-Z, -X * 1/2-Y, 1/2-Z, +X 1/2+Y, 1/2+X, -Z * 1/2-Y, 1/2-X, -Z * 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-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+Y, +X * 1/2-Z, 1/2-Y, -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-Z, 1/2+X, +Y * 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-Z, +X * 1/2-Y, 1/2+Z, +X * 1/2+Y, 1/2+Z, -X 1/2-Y, 1/2-X, +Z * 1/2+Y, 1/2+X, +Z * 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+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-Y, -X * 1/2+Z, 1/2+Y, +X 229 48 24 Im-3m PG432 X, Y, Z * -X, -Y, Z -X, Y, -Z * X, -Y, -Z Z, X, Y * Z, -X, -Y -Z, -X, Y * -Z, X, -Y Y, Z, X * -Y, Z, -X Y, -Z, -X * -Y, -Z, X Y, X, -Z * -Y, -X, -Z Y, -X, Z * -Y, X, Z X, Z, -Y * -X, Z, Y -X, -Z, -Y * X, -Z, Y Z, Y, -X * Z, -Y, X -Z, Y, X * -Z, -Y, -X -X, -Y, -Z * X, Y, -Z X, -Y, Z * -X, Y, Z -Z, -X, -Y * -Z, X, Y Z, X, -Y * Z, -X, Y -Y, -Z, -X * Y, -Z, X -Y, Z, X * Y, Z, -X -Y, -X, Z * Y, X, Z -Y, X, -Z * Y, -X, -Z -X, -Z, Y * X, -Z, -Y X, Z, Y * -X, Z, -Y -Z, -Y, X * -Z, Y, -X 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 * X+1/2, -Y+1/2, -Z+1/2 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