Crystallographic Space Group Symmetry Tables


Triclinic

  • 1 P1
  • 2 P-1

    Monoclinic

  • 3 P2
  • 4 P2(1)
  • 5 C2
  • 6 Pm
  • 7 Pc
  • 8 Cm
  • 9 Cc
  • 10 P2/m
  • 11 P2(1)/m
  • 12 C2/m
  • 13 P2/c
  • 14 P2(1)/c
  • 15 C2/c

    Orthorhombic

  • 16 P222
  • 17 P222(1)
  • 18 P2(1)2(1)2
  • 19 P2(1)2(1)2(1)
  • 20 C222(1)
  • 21 C222
  • 22 F222
  • 23 I222
  • 24 I2(1)2(1)2(1)
  • 25 Pmm2
  • 26 Pmc2(1)
  • 27 Pcc2
  • 28 Pma2
  • 29 Pca2(1)
  • 30 Pnc2
  • 31 Pmn2(1)
  • 32 Pba2
  • 33 Pna2(1)
  • 34 Pnn2
  • 35 Cmm2
  • 36 Cmc2(1)
  • 37 Ccc2
  • 38 Amm2
  • 39 Abm2
  • 40 Ama2
  • 41 Aba2
  • 42 Fmm2
  • 43 Fdd2
  • 44 Imm2
  • 45 Iba2
  • 46 Ima2
  • 47 Pmmm
  • 48 Pnnn
  • 49 Pccm
  • 50 Pban
  • 51 Pmma
  • 52 Pnna
  • 53 Pmna
  • 54 Pcca
  • 55 Pbam
  • 56 Pccn
  • 57 Pbcm
  • 58 Pnnm
  • 59 Pmmn
  • 60 Pbcn
  • 61 Pbca
  • 62 Pnma
  • 63 Cmcm
  • 64 Cmca
  • 65 Cmmm
  • 66 Cccm
  • 67 Cmma
  • 68 Ccca
  • 69 Fmmm
  • 70 Fddd
  • 71 Immm
  • 72 Ibam
  • 73 Ibca
  • 74 Imma

    Tetragonal

  • 75 P4
  • 76 P4(1)
  • 77 P4(2)
  • 78 P4(3)
  • 79 I4
  • 80 I4(1)
  • 81 P-4
  • 82 I-4
  • 83 P4/m
  • 84 P4(2)/m
  • 85 P4/n
  • 86 P4(2)/n
  • 87 I4/m
  • 88 I4(1)/a
  • 89 P422
  • 90 P42(1)2
  • 91 P4(1)22
  • 92 P4(1)2(1)2
  • 93 P4(2)22
  • 94 P4(2)2(1)2
  • 95 P4(3)22
  • 96 P4(3)2(1)2
  • 97 I422
  • 98 I4(1)22
  • 99 P4mm
  • 100 P4bm
  • 101 P4(2)cm
  • 102 P4(2)nm
  • 103 P4cc
  • 104 P4nc
  • 105 P4(2)mc
  • 106 P4(2)bc
  • 107 I4mm
  • 108 I4cm
  • 109 I4(1)md
  • 110 I4(1)cd
  • 111 P-42m
  • 112 P-42c
  • 113 P-42(1)m
  • 114 P-42(1)c
  • 115 P-4m2
  • 116 P-4c2
  • 117 P-4b2
  • 118 P-4n2
  • 119 I-4m2
  • 120 I-4c2
  • 121 I-42m
  • 122 I-42d
  • 123 P4/mmm
  • 124 P4/mcc
  • 125 P4/nbm
  • 126 P4/nnc
  • 127 P4/mbm
  • 128 P4/mnc
  • 129 P4/nmm
  • 130 P4/ncc
  • 131 P4(2)/mmc
  • 132 P4(2)/mcm
  • 133 P4(2)/nbc
  • 134 P4(2)/nnm
  • 135 P4(2)/mbc
  • 136 P4(2)/mnm
  • 137 P4(2)/nmc
  • 138 P4(2)/ncm
  • 139 I4/mmm
  • 140 I4/mcm
  • 141 I4(1)/amd
  • 142 I4(1)/acd

    Trigonal

  • 143 P3
  • 144 P3(1)
  • 145 P3(2)
  • 146 R3
  • 147 P-3
  • 148 R-3
  • 149 P312
  • 150 P321
  • 151 P3(1)12
  • 152 P3(1)21
  • 153 P3(2)12
  • 154 P3(2)21
  • 155 R32
  • 156 P3m1
  • 157 P31m
  • 158 P3c1
  • 159 P31c
  • 160 R3m
  • 161 R3c
  • 162 P-31m
  • 163 P-31c
  • 164 P-3m1
  • 165 P-3c1
  • 166 R-3m
  • 167 R-3c

    Hexagonal

  • 168 P6
  • 169 P6(1)
  • 170 P6(5)
  • 171 P6(2)
  • 172 P6(4)
  • 173 P6(3)
  • 174 P-6
  • 175 P6/m
  • 176 P6(3)/m
  • 177 P622
  • 178 P6(1)22
  • 179 P6(5)22
  • 180 P6(2)22
  • 181 P6(4)22
  • 182 P6(3)22
  • 183 P6mm
  • 184 P6cc
  • 185 P6(3)cm
  • 186 P6(3)mc
  • 187 P-6m2
  • 188 P-6c2
  • 189 P-62m
  • 190 P-62c
  • 191 P6/mmm
  • 192 P6/mcc
  • 193 P6(3)/mcm
  • 194 P6(3)/mmc

    Cubic

  • 195 P23
  • 196 F23
  • 197 I23
  • 198 P2(1)3
  • 199 I2(1)3
  • 200 Pm-3
  • 201 Pn-3
  • 202 Fm-3
  • 203 Fd-3
  • 204 Im-3
  • 205 Pa-3
  • 206 Ia-3
  • 207 P432
  • 208 P4(2)32
  • 209 F432
  • 210 F4(1)32
  • 211 I432
  • 212 P4(3)32
  • 213 P4(1)32
  • 214 I4(1)32
  • 215 P-43m
  • 216 F4-3m
  • 217 I-43m
  • 218 P-43n
  • 219 F-43c
  • 220 I-43d
  • 221 Pm-3m
  • 222 Pn-3n
  • 223 Pm-3n
  • 224 Pn-3m
  • 225 Fm-3m
  • 226 Fm-3c
  • 227 Fd-3m
  • 228 Fd-3c
  • 229 Im-3m
  • 230 Ia-3d

    1 P1

  • Number of Symmetry Operators = 1
  • Space Group Name = P1
  • Crystal System = TRICLINIC
  • Laue Class = -1
  • Point Group = 1
  • Patterson Space Group # = 2
  • Lattice Type = P
  • symmetry= X,Y,Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1
  • 2 P-1

  • Number of Symmetry Operators = 2
  • Space Group Name = P-1
  • Crystal System = TRICLINIC
  • Laue Class = -1
  • Point Group = -1
  • Patterson Space Group # = 2
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1
  • 3 P2

  • Number of Symmetry Operators = 2
  • Space Group Name = P2
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,Y,-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/2
  • 4 P2(1)

  • Number of Symmetry Operators = 2
  • Space Group Name = P2(1)
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,Y+1/2,-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/2
  • 5 C2

  • Number of Symmetry Operators = 4
  • Space Group Name = C2
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2
  • Patterson Space Group # = 12
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 6 Pm

  • Number of Symmetry Operators = 2
  • Space Group Name = Pm
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = m
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= X,-Y,Z
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1
  • 7 Pc

  • Number of Symmetry Operators = 2
  • Space Group Name = Pc
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = m
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= X,-Y,1/2+Z
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1
  • 8 Cm

  • Number of Symmetry Operators = 4
  • Space Group Name = Cm
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = m
  • Patterson Space Group # = 12
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= X,-Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • asymm= 0<=x<=1 and 0<=y<=1/4 and 0<=z<=1
  • 9 Cc

  • Number of Symmetry Operators = 4
  • Space Group Name = Cc
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = m
  • Patterson Space Group # = 12
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • asymm= 0<=x<=1 and 0<=y<=1/4 and 0<=z<=1
  • 10 P2/m

  • Number of Symmetry Operators = 4
  • Space Group Name = P2/m
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2/m
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= -X,-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 11 P2(1)/m

  • Number of Symmetry Operators = 4
  • Space Group Name = P2(1)/m
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2/m
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,1/2+Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,1/2-Y,Z
  • asymm= 0<=x<=1 and 0<=y<=1/4 and 0<=z<=1
  • 12 C2/m

  • Number of Symmetry Operators = 8
  • Space Group Name = C2/m
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2/m
  • Patterson Space Group # = 12
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and 0<=z<=1
  • 13 P2/c

  • Number of Symmetry Operators = 4
  • Space Group Name = P2/c
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2/m
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,-Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/2
  • 14 P2(1)/c

  • Number of Symmetry Operators = 4
  • Space Group Name = P2(1)/c
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2/m
  • Patterson Space Group # = 10
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,-Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • asymm= 0<=x<=1 and 0<=y<=1/4 and 0<=z<=1
  • 15 C2/c

  • Number of Symmetry Operators = 8
  • Space Group Name = C2/c
  • Crystal System = MONOCLINIC
  • Laue Class = 2/m
  • Point Group = 2/m
  • Patterson Space Group # = 12
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 16 P222

  • Number of Symmetry Operators = 4
  • Space Group Name = P222
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 17 P222(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = P222(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 1017 P2(1)22
  • non-standard-origin)
  • Number of Symmetry Operators = 4
  • Space Group Name = P2(1)22
  • Crystal System =
  • non-standard-origin)
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2+X,-Y,-Z
  • symmetry= 1/2-X,-Y,Z
  • symmetry= X,Y,-Z
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1/2
  • 18 P2(1)2(1)2

  • Number of Symmetry Operators = 4
  • Space Group Name = P2(1)2(1)2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 1018 P2(1)2(1)2
  • non-standard-origin)
  • Number of Symmetry Operators = 4
  • Space Group Name = P2(1)2(1)2
  • Crystal System =
  • non-standard-origin)
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,1/2+Y,-Z
  • symmetry= 1/2+X,-Y,-Z
  • symmetry= 1/2-X,1/2-Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 19 P2(1)2(1)2(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = P2(1)2(1)2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 20 C222(1)

  • Number of Symmetry Operators = 8
  • Space Group Name = C222(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 21 C222

  • Number of Symmetry Operators = 8
  • Space Group Name = C222
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1
  • 22 F222

  • Number of Symmetry Operators = 16
  • Space Group Name = F222
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 69
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/4 and 0<=z<=1
  • 23 I222

  • Number of Symmetry Operators = 8
  • Space Group Name = I222
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,Y,-Z
  • symmetry= X+1/2,Y+1/2,Z+1/2
  • symmetry= -X+1/2,-Y+1/2,Z+1/2
  • symmetry= X+1/2,-Y+1/2,-Z+1/2
  • symmetry= -X+1/2,Y+1/2,-Z+1/2
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 24 I2(1)2(1)2(1)

  • Number of Symmetry Operators = 8
  • Space Group Name = I2(1)2(1)2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = 222
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= 1/2-X,Y,-Z
  • symmetry= X,-Y,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 25 Pmm2

  • Number of Symmetry Operators = 4
  • Space Group Name = Pmm2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 26 Pmc2(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = Pmc2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 27 Pcc2

  • Number of Symmetry Operators = 4
  • Space Group Name = Pcc2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 28 Pma2

  • Number of Symmetry Operators = 4
  • Space Group Name = Pma2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= 1/2-X,Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1 and 0<=z<=1
  • 29 Pca2(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = Pca2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= 1/2-X,Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1 and 0<=z<=1
  • 30 Pnc2

  • Number of Symmetry Operators = 4
  • Space Group Name = Pnc2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/2
  • 31 Pmn2(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = Pmn2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= -X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 32 Pba2

  • Number of Symmetry Operators = 4
  • Space Group Name = Pba2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 33 Pna2(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = Pna2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 34 Pnn2

  • Number of Symmetry Operators = 4
  • Space Group Name = Pnn2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 35 Cmm2

  • Number of Symmetry Operators = 8
  • Space Group Name = Cmm2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1
  • 36 Cmc2(1)

  • Number of Symmetry Operators = 8
  • Space Group Name = Cmc2(1)
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 37 Ccc2

  • Number of Symmetry Operators = 8
  • Space Group Name = Ccc2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1
  • 38 Amm2

  • Number of Symmetry Operators = 8
  • Space Group Name = Amm2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = A
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 39 Abm2

  • Number of Symmetry Operators = 8
  • Space Group Name = Abm2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = A
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,1/2-Y,Z
  • symmetry= -X,1/2+Y,Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and 0<=z<=1
  • 40 Ama2

  • Number of Symmetry Operators = 8
  • Space Group Name = Ama2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = A
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= 1/2-X,Y,Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1
  • 41 Aba2

  • Number of Symmetry Operators = 8
  • Space Group Name = Aba2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 65
  • Lattice Type = A
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 42 Fmm2

  • Number of Symmetry Operators = 16
  • Space Group Name = Fmm2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 69
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/4 and 0<=z<=1
  • 43 Fdd2

  • Number of Symmetry Operators = 16
  • Space Group Name = Fdd2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 69
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/4+X,1/4-Y,1/4+Z
  • symmetry= 1/4-X,1/4+Y,1/4+Z
  • {*!!*}
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= 1/4+X,3/4-Y,3/4+Z
  • symmetry= 1/4-X,3/4+Y,3/4+Z
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 3/4+X,1/4-Y,3/4+Z
  • symmetry= 3/4-X,1/4+Y,3/4+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 3/4+X,3/4-Y,1/4+Z
  • symmetry= 3/4-X,3/4+Y,1/4+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/4 and 0<=z<=1
  • 44 Imm2

  • Number of Symmetry Operators = 8
  • Space Group Name = Imm2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 45 Iba2

  • Number of Symmetry Operators = 8
  • Space Group Name = Iba2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 46 Ima2

  • Number of Symmetry Operators = 8
  • Space Group Name = Ima2
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mm2
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= 1/2-X,Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1 and 0<=z<=1/2
  • 47 Pmmm

  • Number of Symmetry Operators = 8
  • Space Group Name = Pmmm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 48 Pnnn

  • Number of Symmetry Operators = 8
  • Space Group Name = Pnnn
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1
  • 49 Pccm

  • Number of Symmetry Operators = 8
  • Space Group Name = Pccm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 50 Pban

  • Number of Symmetry Operators = 8
  • Space Group Name = Pban
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 51 Pmma

  • Number of Symmetry Operators = 8
  • Space Group Name = Pmma
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= 1/2+X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= 1/2-X,Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1
  • 52 Pnna

  • Number of Symmetry Operators = 8
  • Space Group Name = Pnna
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1 and 0<=y<=1/4 and 0<=z<=1/2
  • 53 Pmna

  • Number of Symmetry Operators = 8
  • Space Group Name = Pmna
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= -X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 54 Pcca

  • Number of Symmetry Operators = 8
  • Space Group Name = Pcca
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 55 Pbam

  • Number of Symmetry Operators = 8
  • Space Group Name = Pbam
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 56 Pccn

  • Number of Symmetry Operators = 8
  • Space Group Name = Pccn
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1 and 0<=z<=1/2
  • 57 Pbcm

  • Number of Symmetry Operators = 8
  • Space Group Name = Pbcm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 58 Pnnm

  • Number of Symmetry Operators = 8
  • Space Group Name = Pnnm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 59 Pmmn

  • Number of Symmetry Operators = 8
  • Space Group Name = Pmmn
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,Y+1/2,-Z
  • symmetry= X+1/2,1/2-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= X+1/2,Y+1/2,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 1059 Pmmn
  • non-standard-origin)
  • Number of Symmetry Operators = 8
  • Space Group Name = Pmmn
  • Crystal System =
  • non-standard-origin)
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= -X,1/2+Y,-Z
  • symmetry= 1/2+X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X+1/2,Y+1/2,-Z
  • symmetry= X,1/2-Y,Z
  • symmetry= 1/2-X,Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 60 Pbcn

  • Number of Symmetry Operators = 8
  • Space Group Name = Pbcn
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 61 Pbca

  • Number of Symmetry Operators = 8
  • Space Group Name = Pbca
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 62 Pnma

  • Number of Symmetry Operators = 8
  • Space Group Name = Pnma
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 47
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X+1/2,-Y,Z+1/2
  • symmetry= -X,Y+1/2,-Z
  • symmetry= X+1/2,-Y+1/2,-Z+1/2
  • symmetry= -X,-Y,-Z
  • symmetry= X+1/2,Y,-Z+1/2
  • symmetry= X,-Y+1/2,Z
  • symmetry= -X+1/2,Y+1/2,Z+1/2
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and 0<=z<=1
  • 63 Cmcm

  • Number of Symmetry Operators = 16
  • Space Group Name = Cmcm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,1/2-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 64 Cmca

  • Number of Symmetry Operators = 16
  • Space Group Name = Cmca
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 65 Cmmm

  • Number of Symmetry Operators = 16
  • Space Group Name = Cmmm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 66 Cccm

  • Number of Symmetry Operators = 16
  • Space Group Name = Cccm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 67 Cmma

  • Number of Symmetry Operators = 16
  • Space Group Name = Cmma
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= -X,1/2+Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,1/2+Y,-Z
  • symmetry= X,1/2-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,-Y,Z
  • symmetry= 1/2-X,Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,Y,-Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and 0<=z<=1/2
  • 68 Ccca

  • Number of Symmetry Operators = 16
  • Space Group Name = Ccca
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 65
  • Lattice Type = C
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= -X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2-X,-Y,1/2-Z
  • symmetry= X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 69 Fmmm

  • Number of Symmetry Operators = 32
  • Space Group Name = Fmmm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 69
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= -X,1/2-Y,1/2-Z
  • symmetry= X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2-X,-Y,1/2-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/4 and 0<=z<=1/2
  • 70 Fddd

  • Number of Symmetry Operators = 32
  • Space Group Name = Fddd
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 69
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/4-X,1/4-Y,1/4-Z
  • symmetry= 1/4+X,1/4+Y,1/4-Z
  • symmetry= 1/4+X,1/4-Y,1/4+Z
  • symmetry= 1/4-X,1/4+Y,1/4+Z
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= 1/4-X,3/4-Y,3/4-Z
  • symmetry= 1/4+X,3/4+Y,3/4-Z
  • symmetry= 1/4+X,3/4-Y,3/4+Z
  • symmetry= 1/4-X,3/4+Y,3/4+Z
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 3/4-X,1/4-Y,3/4-Z
  • symmetry= 3/4+X,1/4+Y,3/4-Z
  • symmetry= 3/4+X,1/4-Y,3/4+Z
  • symmetry= 3/4-X,1/4+Y,3/4+Z
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 3/4-X,3/4-Y,1/4-Z
  • symmetry= 3/4+X,3/4+Y,1/4-Z
  • symmetry= 3/4+X,3/4-Y,1/4+Z
  • symmetry= 3/4-X,3/4+Y,1/4+Z
  • asymm= 0<=x<=1/8 and 0<=y<=1/4 and 0<=z<=1
  • 71 Immm

  • Number of Symmetry Operators = 16
  • Space Group Name = Immm
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 72 Ibam

  • Number of Symmetry Operators = 16
  • Space Group Name = Ibam
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 73 Ibca

  • Number of Symmetry Operators = 16
  • Space Group Name = Ibca
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= 1/2-X,Y,-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= X,1/2+Y,-Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= -X,Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1/2
  • 74 Imma

  • Number of Symmetry Operators = 16
  • Space Group Name = Imma
  • Crystal System = ORTHORHOMBIC
  • Laue Class = mmm
  • Point Group = mmm
  • Patterson Space Group # = 71
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= -X,1/2+Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,1/2+Y,-Z
  • symmetry= X,1/2-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/4 and 0<=z<=1
  • 75 P4

  • Number of Symmetry Operators = 4
  • Space Group Name = P4
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 76 P4(1)

  • Number of Symmetry Operators = 4
  • Space Group Name = P4(1)
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -Y,X,1/4+Z
  • symmetry= Y,-X,3/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 77 P4(2)

  • Number of Symmetry Operators = 4
  • Space Group Name = P4(2)
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 78 P4(3)

  • Number of Symmetry Operators = 4
  • Space Group Name = P4(3)
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -Y,X,3/4+Z
  • symmetry= Y,-X,1/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 79 I4

  • Number of Symmetry Operators = 8
  • Space Group Name = I4
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4
  • Patterson Space Group # = 87
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 80 I4(1)

  • Number of Symmetry Operators = 8
  • Space Group Name = I4(1)
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4
  • Patterson Space Group # = 87
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 81 P-4

  • Number of Symmetry Operators = 4
  • Space Group Name = P-4
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = -4
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1
  • 82 I-4

  • Number of Symmetry Operators = 8
  • Space Group Name = I-4
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = -4
  • Patterson Space Group # = 87
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 83 P4/m

  • Number of Symmetry Operators = 8
  • Space Group Name = P4/m
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4/m
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 84 P4(2)/m

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)/m
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4/m
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,1/2-Z
  • symmetry= -Y,X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 85 P4/n

  • Number of Symmetry Operators = 8
  • Space Group Name = P4/n
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4/m
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,Z
  • symmetry= 1/2+Y,1/2-X,Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 86 P4(2)/n

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)/n
  • Crystal System = TETRAGOANL
  • Laue Class = 4/m
  • Point Group = 4/m
  • Patterson Space Group # = 83
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 87 I4/m

  • Number of Symmetry Operators = 16
  • Space Group Name = I4/m
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4/m
  • Patterson Space Group # = 87
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 88 I4(1)/a

  • Number of Symmetry Operators = 16
  • Space Group Name = I4(1)/a
  • Crystal System = TETRAGONAL
  • Laue Class = 4/m
  • Point Group = 4/m
  • Patterson Space Group # = 87
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= -X,1/2-Y,1/4-Z
  • symmetry= 1/2+X,Y,3/4-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • symmetry= 1/2-X,-Y,3/4-Z
  • symmetry= X,1/2+Y,1/4-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= -Y,X,-Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/4 and 0<=z<=1
  • 89 P422

  • Number of Symmetry Operators = 8
  • Space Group Name = P422
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 90 P42(1)2

  • Number of Symmetry Operators = 8
  • Space Group Name = P42(1)2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,Z
  • symmetry= 1/2+Y,1/2-X,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 91 P4(1)22

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(1)22
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -Y,X,1/4+Z
  • symmetry= Y,-X,3/4+Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= Y,X,3/4-Z
  • symmetry= -Y,-X,1/4-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/8
  • 92 P4(1)2(1)2

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(1)2(1)2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,1/2-X,3/4+Z
  • symmetry= 1/2-X,1/2+Y,1/4-Z
  • symmetry= 1/2+X,1/2-Y,3/4-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,1/2-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/8
  • 93 P4(2)22

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)22
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 94 P4(2)2(1)2

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)2(1)2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 95 P4(3)22

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(3)22
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= -Y,X,3/4+Z
  • symmetry= Y,-X,1/4+Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= Y,X,1/4-Z
  • symmetry= -Y,-X,3/4-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/8
  • 96 P4(3)2(1)2

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(3)2(1)2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,3/4+Z
  • symmetry= 1/2+Y,1/2-X,1/4+Z
  • symmetry= 1/2-X,1/2+Y,3/4-Z
  • symmetry= 1/2+X,1/2-Y,1/4-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,1/2-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/8
  • 97 I422

  • Number of Symmetry Operators = 16
  • Space Group Name = I422
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 98 I4(1)22

  • Number of Symmetry Operators = 16
  • Space Group Name = I4(1)22
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 422
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= 1/2-X,Y,3/4-Z
  • symmetry= X,1/2-Y,1/4-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • symmetry= -X,1/2+Y,1/4-Z
  • symmetry= 1/2+X,-Y,3/4-Z
  • symmetry= Y,X,-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/8
  • 99 P4mm

  • Number of Symmetry Operators = 8
  • Space Group Name = P4mm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1 and x<=y
  • 100 P4bm

  • Number of Symmetry Operators = 8
  • Space Group Name = P4bm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1 and y<=1/2-x
  • 101 P4(2)cm

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)cm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1 and x<=y
  • 102 P4(2)nm

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)nm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1 and x<=y
  • 103 P4cc

  • Number of Symmetry Operators = 8
  • Space Group Name = P4cc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 104 P4nc

  • Number of Symmetry Operators = 8
  • Space Group Name = P4nc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 105 P4(2)mc

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)mc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 106 P4(2)bc

  • Number of Symmetry Operators = 8
  • Space Group Name = P4(2)bc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 107 I4mm

  • Number of Symmetry Operators = 16
  • Space Group Name = I4mm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and x<=y
  • 108 I4cm

  • Number of Symmetry Operators = 16
  • Space Group Name = I4cm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=1/2-x
  • 109 I4(1)md

  • Number of Symmetry Operators = 16
  • Space Group Name = I4(1)md
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= -Y,1/2-X,1/4+Z
  • symmetry= 1/2+Y,X,3/4+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2-Y,-X,3/4+Z
  • symmetry= Y,1/2+X,1/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 110 I4(1)cd

  • Number of Symmetry Operators = 16
  • Space Group Name = I4(1)cd
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4mm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= -Y,1/2-X,3/4+Z
  • symmetry= 1/2+Y,X,1/4+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2-Y,-X,1/4+Z
  • symmetry= Y,1/2+X,3/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 111 P-42m

  • Number of Symmetry Operators = 8
  • Space Group Name = P-42m
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1 and x<=y
  • 112 P-42c

  • Number of Symmetry Operators = 8
  • Space Group Name = P-42c
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 113 P-42(1)m

  • Number of Symmetry Operators = 8
  • Space Group Name = P-42(1)m
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1 and y<=1/2-x
  • 114 P-42(1)c

  • Number of Symmetry Operators = 8
  • Space Group Name = P-42(1)c
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 115 P-4m2

  • Number of Symmetry Operators = 8
  • Space Group Name = P-4m2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,-X,-Z
  • {**}
  • symmetry= -Y,X,-Z
  • {**}
  • symmetry= X,-Y,Z
  • {**}
  • symmetry= -X,Y,Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 116 P-4c2

  • Number of Symmetry Operators = 8
  • Space Group Name = P-4c2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 117 P-4b2

  • Number of Symmetry Operators = 8
  • Space Group Name = P-4b2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2+Y,1/2+X,-Z
  • symmetry= 1/2-Y,1/2-X,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2
  • 118 P-4n2

  • Number of Symmetry Operators = 8
  • Space Group Name = P-4n2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4
  • 119 I-4m2

  • Number of Symmetry Operators = 16
  • Space Group Name = I-4m2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 120 I-4c2

  • Number of Symmetry Operators = 16
  • Space Group Name = I-4c2
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= Y,X,1/2-Z
  • {***}
  • symmetry= -Y,-X,1/2-Z
  • symmetry= X+1/2,Y+1/2,Z+1/2
  • symmetry= -X+1/2,-Y+1/2,Z+1/2
  • symmetry= Y+1/2,-X+1/2,-Z+1/2
  • symmetry= -Y+1/2,X+1/2,-Z+1/2
  • symmetry= X+1/2,-Y+1/2,Z
  • symmetry= -X+1/2,Y+1/2,Z
  • symmetry= Y+1/2,X+1/2,-Z
  • {***}
  • symmetry= -Y+1/2,-X+1/2,-Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 121 I-42m

  • Number of Symmetry Operators = 16
  • Space Group Name = I-42m
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and x<=y
  • 122 I-42d

  • Number of Symmetry Operators = 16
  • Space Group Name = I-42d
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = -42m
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2-X,Y,3/4-Z
  • symmetry= 1/2+X,-Y,3/4-Z
  • symmetry= 1/2-Y,-X,3/4+Z
  • symmetry= 1/2+Y,X,3/4+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= -X,1/2+Y,1/4-Z
  • symmetry= X,1/2-Y,1/4-Z
  • symmetry= -Y,1/2-X,1/4+Z
  • symmetry= Y,1/2+X,1/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/8
  • 123 P4/mmm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/mmm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and x<=y
  • 124 P4/mcc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/mcc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 125 P4/nbm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/nbm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= 1/2+Y,1/2-X,-Z
  • symmetry= 1/2-Y,1/2+X,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=1/2-x
  • 126 P4/nnc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/nnc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 127 P4/mbm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/mbm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Y,1/2+X,-Z
  • symmetry= 1/2-Y,1/2-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=1/2-x
  • 128 P4/mnc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/mnc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 129 P4/nmm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/nmm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,Z
  • symmetry= 1/2+Y,1/2-X,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=1/2-x
  • 130 P4/ncc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4/ncc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,Z
  • symmetry= 1/2+Y,1/2-X,Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 131 P4(2)/mmc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/mmc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,1/2-Z
  • symmetry= -Y,X,1/2-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 132 P4(2)/mcm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/mcm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,1/2-Z
  • symmetry= -Y,X,1/2-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and x<=y
  • 133 P4(2)/nbc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/nbc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= 1/2+Y,1/2+X,-Z
  • symmetry= 1/2-Y,1/2-X,-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 134 P4(2)/nnm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/nnm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1 and 0<=z<=1/4 and x<=y and y<=1-x
  • 135 P4(2)/mbc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/mbc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,1/2+Z
  • symmetry= Y,-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,1/2-Z
  • symmetry= -Y,X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 136 P4(2)/mnm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/mnm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X+1/2,Z+1/2
  • symmetry= Y+1/2,1/2-X,Z+1/2
  • symmetry= 1/2-X,Y+1/2,1/2-Z
  • symmetry= X+1/2,1/2-Y,1/2-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y+1/2,1/2-X,1/2-Z
  • symmetry= 1/2-Y,X+1/2,1/2-Z
  • symmetry= X+1/2,1/2-Y,Z+1/2
  • symmetry= 1/2-X,Y+1/2,Z+1/2
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and x<=y
  • 137 P4(2)/nmc

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/nmc
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4
  • 138 P4(2)/ncm

  • Number of Symmetry Operators = 16
  • Space Group Name = P4(2)/ncm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 123
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/4 and 0<=y<=1/2 and 0<=z<=1 and x<=y and y<=1/2-x
  • 139 I4/mmm

  • Number of Symmetry Operators = 32
  • Space Group Name = I4/mmm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4 and x<=y
  • 140 I4/mcm

  • Number of Symmetry Operators = 32
  • Space Group Name = I4/mcm
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -Y,X,Z
  • symmetry= Y,-X,Z
  • symmetry= -X,Y,1/2-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,X,1/2+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Y,1/2+X,-Z
  • symmetry= 1/2-Y,1/2-X,-Z
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2+X,Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4 and y<=1/2-x
  • 141 I4(1)/amd

  • Number of Symmetry Operators = 32
  • Space Group Name = I4(1)/amd
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= 1/2-X,Y,3/4-Z
  • symmetry= X,1/2-Y,1/4-Z
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= -Y,-X,-Z
  • symmetry= -X,1/2-Y,1/4-Z
  • symmetry= 1/2+X,Y,3/4-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= -X,Y,Z
  • symmetry= 1/2-Y,-X,3/4+Z
  • symmetry= Y,1/2+X,1/4+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • symmetry= -X,1/2+Y,1/4-Z
  • symmetry= 1/2+X,-Y,3/4-Z
  • symmetry= Y,X,-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2-X,-Y,3/4-Z
  • symmetry= X,1/2+Y,1/4-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= -Y,1/2-X,1/4+Z
  • symmetry= 1/2+Y,X,3/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/8
  • 142 I4(1)/acd

  • Number of Symmetry Operators = 32
  • Space Group Name = I4(1)/acd
  • Crystal System = TETRAGONAL
  • Laue Class = 4/mmm
  • Point Group = 4/mmm
  • Patterson Space Group # = 139
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= -Y,1/2+X,1/4+Z
  • symmetry= 1/2+Y,-X,3/4+Z
  • symmetry= 1/2-X,Y,1/4-Z
  • symmetry= X,1/2-Y,3/4-Z
  • symmetry= 1/2+Y,1/2+X,-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= -X,1/2-Y,1/4-Z
  • symmetry= 1/2+X,Y,3/4-Z
  • symmetry= Y,-X,-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2-Y,-X,1/4+Z
  • symmetry= Y,1/2+X,3/4+Z
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-Y,X,3/4+Z
  • symmetry= Y,1/2-X,1/4+Z
  • symmetry= -X,1/2+Y,3/4-Z
  • symmetry= 1/2+X,-Y,1/4-Z
  • symmetry= Y,X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,-Z
  • symmetry= 1/2-X,-Y,3/4-Z
  • symmetry= X,1/2+Y,1/4-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= -Y,1/2-X,3/4+Z
  • symmetry= 1/2+Y,X,1/4+Z
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/8
  • 143 P3

  • Number of Symmetry Operators = 3
  • Space Group Name = P3
  • Crystal System = TRIGONAL
  • Laue Class = -3
  • Point Group = 3
  • Patterson Space Group # = 147
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 144 P3(1)

  • Number of Symmetry Operators = 3
  • Space Group Name = P3(1)
  • Crystal System = TRIGONAL
  • Laue Class = -3
  • Point Group = 3
  • Patterson Space Group # = 147
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z+1/3
  • symmetry= Y-X,-X,Z+2/3
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/3
  • 145 P3(2)

  • Number of Symmetry Operators = 3
  • Space Group Name = P3(2)
  • Crystal System = TRIGONAL
  • Laue Class = -3
  • Point Group = 3
  • Patterson Space Group # = 147
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z+2/3
  • symmetry= Y-X,-X,Z+1/3
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/3
  • 146 R3

  • Number of Symmetry Operators = 9
  • Space Group Name = R3
  • Crystal System = TRIGONAL
  • Laue Class = -3
  • Point Group = 3
  • Patterson Space Group # = 148
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= X+2/3,Y+1/3,Z+1/3
  • symmetry= -Y+2/3,X-Y+1/3,Z+1/3
  • symmetry= Y-X+2/3,-X+1/3,Z+1/3
  • symmetry= X+1/3,Y+2/3,Z+2/3
  • symmetry= -Y+1/3,X-Y+2/3,Z+2/3
  • symmetry= Y-X+1/3,-X+2/3,Z+2/3
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/3 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 147 P-3

  • Number of Symmetry Operators = 6
  • Space Group Name = P-3
  • Crystal System = TRIGONAL
  • Laue Class = -3
  • Point Group = -3
  • Patterson Space Group # = 147
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 148 R-3

  • Number of Symmetry Operators = 18
  • Space Group Name = R-3
  • Crystal System = TRIGONAL
  • Laue Class = -3
  • Point Group = -3
  • Patterson Space Group # = 148
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= 2/3+X,1/3+Y,1/3+Z
  • symmetry= 2/3-Y,1/3+X-Y,1/3+Z
  • symmetry= 2/3+Y-X,1/3-X,1/3+Z
  • symmetry= 2/3-X,1/3-Y,1/3-Z
  • symmetry= 2/3+Y,1/3+Y-X,1/3-Z
  • symmetry= 2/3+X-Y,1/3+X,1/3-Z
  • symmetry= 1/3+X,2/3+Y,2/3+Z
  • symmetry= 1/3-Y,2/3+X-Y,2/3+Z
  • symmetry= 1/3+Y-X,2/3-X,2/3+Z
  • symmetry= 1/3-X,2/3-Y,2/3-Z
  • symmetry= 1/3+Y,2/3+Y-X,2/3-Z
  • symmetry= 1/3+X-Y,2/3+X,2/3-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/6 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 149 P312

  • Number of Symmetry Operators = 6
  • Space Group Name = P312
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 150 P321

  • Number of Symmetry Operators = 6
  • Space Group Name = P321
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 151 P3(1)12

  • Number of Symmetry Operators = 6
  • Space Group Name = P3(1)12
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,1/3+Z
  • symmetry= Y-X,-X,2/3+Z
  • symmetry= -Y,-X,2/3-Z
  • symmetry= Y-X,Y,1/3-Z
  • symmetry= X,X-Y,-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6
  • 152 P3(1)21

  • Number of Symmetry Operators = 6
  • Space Group Name = P3(1)21
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z+1/3
  • symmetry= Y-X,-X,Z+2/3
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,2/3-Z
  • symmetry= -X,Y-X,1/3-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6
  • 153 P3(2)12

  • Number of Symmetry Operators = 6
  • Space Group Name = P3(2)12
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,2/3+Z
  • symmetry= Y-X,-X,1/3+Z
  • symmetry= -Y,-X,1/3-Z
  • symmetry= Y-X,Y,2/3-Z
  • symmetry= X,X-Y,-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6
  • 154 P3(2)21

  • Number of Symmetry Operators = 6
  • Space Group Name = P3(2)21
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z+2/3
  • symmetry= Y-X,-X,Z+1/3
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,1/3-Z
  • symmetry= -X,Y-X,2/3-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6
  • 155 R32

  • Number of Symmetry Operators = 18
  • Space Group Name = R32
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 32
  • Patterson Space Group # = 166
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= 2/3+X,1/3+Y,1/3+Z
  • symmetry= 2/3-Y,1/3+X-Y,1/3+Z
  • symmetry= 2/3+Y-X,1/3-X,1/3+Z
  • symmetry= 2/3+Y,1/3+X,1/3-Z
  • symmetry= 2/3+X-Y,1/3-Y,1/3-Z
  • symmetry= 2/3-X,1/3+Y-X,1/3-Z
  • symmetry= 1/3+X,2/3+Y,2/3+Z
  • symmetry= 1/3-Y,2/3+X-Y,2/3+Z
  • symmetry= 1/3+Y-X,2/3-X,2/3+Z
  • symmetry= 1/3+Y,2/3+X,2/3-Z
  • symmetry= 1/3+X-Y,2/3-Y,2/3-Z
  • symmetry= 1/3-X,2/3+Y-X,2/3-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/6 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 156 P3m1

  • Number of Symmetry Operators = 6
  • Space Group Name = P3m1
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 3m
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1 and x<=2 y and y<=min(1-x,2 x)
  • 157 P31m

  • Number of Symmetry Operators = 6
  • Space Group Name = P31m
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 3m
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1 and x<=(y+1)/2 and y<=min(1-x,x)
  • 158 P3c1

  • Number of Symmetry Operators = 6
  • Space Group Name = P3c1
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 3m
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 159 P31c

  • Number of Symmetry Operators = 6
  • Space Group Name = P31c
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 3m
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 160 R3m

  • Number of Symmetry Operators = 18
  • Space Group Name = R3m
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 3m
  • Patterson Space Group # = 166
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= 2/3+X,1/3+Y,1/3+Z
  • symmetry= 2/3-Y,1/3+X-Y,1/3+Z
  • symmetry= 2/3+Y-X,1/3-X,1/3+Z
  • symmetry= 2/3-Y,1/3-X,1/3+Z
  • symmetry= 2/3+Y-X,1/3+Y,1/3+Z
  • symmetry= 2/3+X,1/3+X-Y,1/3+Z
  • symmetry= 1/3+X,2/3+Y,2/3+Z
  • symmetry= 1/3-Y,2/3+X-Y,2/3+Z
  • {***}
  • symmetry= 1/3+Y-X,2/3-X,2/3+Z
  • symmetry= 1/3-Y,2/3-X,2/3+Z
  • symmetry= 1/3+Y-X,2/3+Y,2/3+Z
  • symmetry= 1/3+X,2/3+X-Y,2/3+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/3 and x<=2 y and y<=min(1-x,2 x)
  • 161 R3c

  • Number of Symmetry Operators = 18
  • Space Group Name = R3c
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = 3m
  • Patterson Space Group # = 166
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= 2/3+X,1/3+Y,1/3+Z
  • symmetry= 2/3-Y,1/3+X-Y,1/3+Z
  • symmetry= 2/3+Y-X,1/3-X,1/3+Z
  • symmetry= 2/3-Y,1/3-X,5/6+Z
  • symmetry= 2/3+Y-X,1/3+Y,5/6+Z
  • symmetry= 2/3+X,1/3+X-Y,5/6+Z
  • symmetry= 1/3+X,2/3+Y,2/3+Z
  • symmetry= 1/3-Y,2/3+X-Y,2/3+Z
  • symmetry= 1/3+Y-X,2/3-X,2/3+Z
  • symmetry= 1/3-Y,2/3-X,1/6+Z
  • symmetry= 1/3+Y-X,2/3+Y,1/6+Z
  • symmetry= 1/3+X,2/3+X-Y,1/6+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/6 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 162 P-31m

  • Number of Symmetry Operators = 12
  • Space Group Name = P-31m
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = -3m
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,x)
  • 163 P-31c

  • Number of Symmetry Operators = 12
  • Space Group Name = P-31c
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = -3m
  • Patterson Space Group # = 162
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= Y-X,Y,1/2-Z
  • symmetry= X,X-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 164 P-3m1

  • Number of Symmetry Operators = 12
  • Space Group Name = P-3m1
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = -3m
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/3 and 0<=z<=1 and x<=(1+y)/2 and y<=x/2
  • 165 P-3c1

  • Number of Symmetry Operators = 12
  • Space Group Name = P-3c1
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = -3m
  • Patterson Space Group # = 164
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,1/2-Z
  • symmetry= X-Y,-Y,1/2-Z
  • symmetry= -X,Y-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 166 R-3m

  • Number of Symmetry Operators = 36
  • Space Group Name = R-3m
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = -3m
  • Patterson Space Group # = 166
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= 2/3+X,1/3+Y,1/3+Z
  • symmetry= 2/3-Y,1/3+X-Y,1/3+Z
  • symmetry= 2/3+Y-X,1/3-X,1/3+Z
  • symmetry= 2/3+Y,1/3+X,1/3-Z
  • symmetry= 2/3+X-Y,1/3-Y,1/3-Z
  • symmetry= 2/3-X,1/3+Y-X,1/3-Z
  • symmetry= 2/3-X,1/3-Y,1/3-Z
  • symmetry= 2/3+Y,1/3+Y-X,1/3-Z
  • symmetry= 2/3+X-Y,1/3+X,1/3-Z
  • symmetry= 2/3-Y,1/3-X,1/3+Z
  • symmetry= 2/3+Y-X,1/3+Y,1/3+Z
  • symmetry= 2/3+X,1/3+X-Y,1/3+Z
  • symmetry= 1/3+X,2/3+Y,2/3+Z
  • symmetry= 1/3-Y,2/3+X-Y,2/3+Z
  • symmetry= 1/3+Y-X,2/3-X,2/3+Z
  • {***}
  • symmetry= 1/3+Y,2/3+X,2/3-Z
  • symmetry= 1/3+X-Y,2/3-Y,2/3-Z
  • symmetry= 1/3-X,2/3+Y-X,2/3-Z
  • symmetry= 1/3-X,2/3-Y,2/3-Z
  • symmetry= 1/3+Y,2/3+Y-X,2/3-Z
  • symmetry= 1/3X-Y,2/3+X,2/3-Z
  • symmetry= 1/3-Y,2/3-X,2/3+Z
  • symmetry= 1/3+Y-X,2/3+Y,2/3+Z
  • symmetry= 1/3+X,2/3+X-Y,2/3+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/6 and x<=2 y and y<=min(1-x,2 x)
  • 167 R-3c

  • Number of Symmetry Operators = 36
  • Space Group Name = R-3c
  • Crystal System = TRIGONAL
  • Laue Class = -3m
  • Point Group = -3m
  • Patterson Space Group # = 166
  • Lattice Type = R
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= Y,X,1/2-Z
  • symmetry= X-Y,-Y,1/2-Z
  • symmetry= -X,Y-X,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= 2/3+X,1/3+Y,1/3+Z
  • symmetry= 2/3-Y,1/3+X-Y,1/3+Z
  • symmetry= 2/3+Y-X,1/3-X,1/3+Z
  • symmetry= 2/3+Y,1/3+X,5/6-Z
  • symmetry= 2/3+X-Y,1/3-Y,5/6-Z
  • symmetry= 2/3-X,1/3+Y-X,5/6-Z
  • symmetry= 2/3-X,1/3-Y,1/3-Z
  • symmetry= 2/3+Y,1/3+Y-X,1/3-Z
  • symmetry= 2/3+X-Y,1/3+X,1/3-Z
  • symmetry= 2/3-Y,1/3-X,5/6+Z
  • symmetry= 2/3+Y-X,1/3+Y,5/6+Z
  • symmetry= 2/3+X,1/3+X-Y,5/6+Z
  • symmetry= 1/3+X,2/3+Y,2/3+Z
  • symmetry= 1/3-Y,2/3+X-Y,2/3+Z
  • symmetry= 1/3+Y-X,2/3-X,2/3+Z
  • symmetry= 1/3+Y,2/3+X,1/6-Z
  • symmetry= 1/3+X-Y,2/3-Y,1/6-Z
  • symmetry= 1/3-X,2/3+Y-X,1/6-Z
  • symmetry= 1/3-X,2/3-Y,2/3-Z
  • symmetry= 1/3+Y,2/3+Y-X,2/3-Z
  • symmetry= 1/3+X-Y,2/3+X,2/3-Z
  • symmetry= 1/3-Y,2/3-X,1/6+Z
  • symmetry= 1/3+Y-X,2/3+Y,1/6+Z
  • symmetry= 1/3+X,2/3+X-Y,1/6+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/12 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 168 P6

  • Number of Symmetry Operators = 6
  • Space Group Name = P6
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1 and x<=(1+y)/2 and y<=min(1-x,x)
  • 169 P6(1)

  • Number of Symmetry Operators = 6
  • Space Group Name = P6(1)
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z+1/3
  • symmetry= Y-X,-X,Z+2/3
  • symmetry= -X,-Y,Z+1/2
  • symmetry= Y,Y-X,Z+5/6
  • symmetry= X-Y,X,Z+1/6
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6
  • 170 P6(5)

  • Number of Symmetry Operators = 6
  • Space Group Name = P6(5)
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z+2/3
  • symmetry= Y-X,-X,Z+1/3
  • symmetry= -X,-Y,Z+1/2
  • symmetry= Y,Y-X,Z+1/6
  • symmetry= X-Y,X,Z+5/6
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6
  • 171 P6(2)

  • Number of Symmetry Operators = 6
  • Space Group Name = P6(2)
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,2/3+Z
  • symmetry= Y-X,-X,1/3+Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,2/3+Z
  • symmetry= X-Y,X,1/3+Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/3 and y<=x
  • 172 P6(4)

  • Number of Symmetry Operators = 6
  • Space Group Name = P6(4)
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,1/3+Z
  • symmetry= Y-X,-X,2/3+Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,1/3+Z
  • symmetry= X-Y,X,2/3+Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/3 and y<=x
  • 173 P6(3)

  • Number of Symmetry Operators = 6
  • Space Group Name = P6(3)
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 174 P-6

  • Number of Symmetry Operators = 6
  • Space Group Name = P-6
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = -6
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= X,Y,-Z
  • symmetry= -Y,X-Y,-Z
  • symmetry= Y-X,-X,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 175 P6/m

  • Number of Symmetry Operators = 12
  • Space Group Name = P6/m
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6/m
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= X,Y,-Z
  • symmetry= -Y,X-Y,-Z
  • symmetry= Y-X,-X,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,x)
  • 176 P6(3)/m

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(3)/m
  • Crystal System = HEXAGONAL
  • Laue Class = 6/m
  • Point Group = 6/m
  • Patterson Space Group # = 175
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= X,Y,1/2-Z
  • symmetry= -Y,X-Y,1/2-Z
  • symmetry= Y-X,-X,1/2-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 177 P622

  • Number of Symmetry Operators = 12
  • Space Group Name = P622
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 622
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,x)
  • 178 P6(1)22

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(1)22
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 622
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,1/3+Z
  • symmetry= Y-X,-X,2/3+Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,5/6+Z
  • symmetry= X-Y,X,1/6+Z
  • symmetry= Y,X,1/3-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,2/3-Z
  • symmetry= -Y,-X,5/6-Z
  • symmetry= Y-X,Y,1/2-Z
  • symmetry= X,X-Y,1/6-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/12
  • 179 P6(5)22

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(5)22
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 622
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,2/3+Z
  • symmetry= Y-X,-X,1/3+Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/6+Z
  • symmetry= X-Y,X,5/6+Z
  • symmetry= Y,X,2/3-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,1/3-Z
  • symmetry= -Y,-X,1/6-Z
  • symmetry= Y-X,Y,1/2-Z
  • symmetry= X,X-Y,5/6-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/12
  • 180 P6(2)22

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(2)22
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 622
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,2/3+Z
  • symmetry= Y-X,-X,1/3+Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,2/3+Z
  • symmetry= X-Y,X,1/3+Z
  • symmetry= Y,X,2/3-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,1/3-Z
  • symmetry= -Y,-X,2/3-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,1/3-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6 and y<=x
  • 181 P6(4)22

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(4)22
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 622
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,1/3+Z
  • symmetry= Y-X,-X,2/3+Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,1/3+Z
  • symmetry= X-Y,X,2/3+Z
  • symmetry= Y,X,1/3-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,2/3-Z
  • symmetry= -Y,-X,1/3-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,2/3-Z
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/6 and y<=x
  • 182 P6(3)22

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(3)22
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 622
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= Y-X,Y,1/2-Z
  • symmetry= X,X-Y,1/2-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 183 P6mm

  • Number of Symmetry Operators = 12
  • Space Group Name = P6mm
  • Crystal System = HEXAGOANL
  • Laue Class = 6/mmm
  • Point Group = 6mm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/3 and 0<=z<=1 and x<=(1+y)/2 and y<=x/2
  • 184 P6cc

  • Number of Symmetry Operators = 12
  • Space Group Name = P6cc
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6mm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,x)
  • 185 P6(3)cm

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(3)cm
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6mm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,x)
  • 186 P6(3)mc

  • Number of Symmetry Operators = 12
  • Space Group Name = P6(3)mc
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6mm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/3 and 0<=z<=1 and x<=(1+y)/2 and y<=x/2
  • 187 P-6m2

  • Number of Symmetry Operators = 12
  • Space Group Name = P-6m2
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = -62m
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= X,Y,-Z
  • symmetry= -Y,X-Y,-Z
  • symmetry= Y-X,-X,-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/2 and x<=2 y and y<=min(1-x,2 x)
  • 188 P-6c2

  • Number of Symmetry Operators = 12
  • Space Group Name = P-6c2
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = -62m
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= X,Y,1/2-Z
  • symmetry= -Y,X-Y,1/2-Z
  • symmetry= Y-X,-X,1/2-Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 189 P-62m

  • Number of Symmetry Operators = 12
  • Space Group Name = P-62m
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = -62m
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= X,Y,-Z
  • symmetry= -Y,X-Y,-Z
  • symmetry= Y-X,-X,-Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/2 and x<=(1+y)/2 and y<=min(1-x,x)
  • 190 P-62c

  • Number of Symmetry Operators = 12
  • Space Group Name = P-62c
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = -62m
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= X,Y,1/2-Z
  • symmetry= -Y,X-Y,1/2-Z
  • symmetry= Y-X,-X,1/2-Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,(1+x)/2)
  • 191 P6/mmm

  • Number of Symmetry Operators = 24
  • Space Group Name = P6/mmm
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6/mmm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y-X,-X,-Z
  • symmetry= -Y,X-Y,-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/3 and 0<=z<=1/2 and x<=(1+y)/2 and y<=x/2
  • 192 P6/mcc

  • Number of Symmetry Operators = 24
  • Space Group Name = P6/mcc
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6/mmm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,Z
  • symmetry= Y,Y-X,Z
  • symmetry= X-Y,X,Z
  • symmetry= Y,X,1/2-Z
  • symmetry= X-Y,-Y,1/2-Z
  • symmetry= -X,Y-X,1/2-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= Y-X,Y,1/2-Z
  • symmetry= X,X-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= X,Y,-Z
  • symmetry= Y-X,-X,-Z
  • symmetry= -Y,X-Y,-Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,x)
  • 193 P6(3)/mcm

  • Number of Symmetry Operators = 24
  • Space Group Name = P6(3)/mcm
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6/mmm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • symmetry= Y,X,1/2-Z
  • symmetry= X-Y,-Y,1/2-Z
  • symmetry= -X,Y-X,1/2-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y-X,Y,-Z
  • symmetry= X,X-Y,-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= X,Y,1/2-Z
  • symmetry= Y-X,-X,1/2-Z
  • symmetry= -Y,X-Y,1/2-Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y-X,Y,1/2+Z
  • symmetry= X,X-Y,1/2+Z
  • symmetry= Y,X,Z
  • symmetry= X-Y,-Y,Z
  • symmetry= -X,Y-X,Z
  • asymm= 0<=x<=2/3 and 0<=y<=1/2 and 0<=z<=1/4 and x<=(1+y)/2 and y<=min(1-x,x)
  • 194 P6(3)/mmc

  • Number of Symmetry Operators = 24
  • Space Group Name = P6(3)/mmc
  • Crystal System = HEXAGONAL
  • Laue Class = 6/mmm
  • Point Group = 6/mmm
  • Patterson Space Group # = 191
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -Y,X-Y,Z
  • symmetry= Y-X,-X,Z
  • symmetry= -X,-Y,1/2+Z
  • symmetry= Y,Y-X,1/2+Z
  • symmetry= X-Y,X,1/2+Z
  • symmetry= Y,X,-Z
  • symmetry= X-Y,-Y,-Z
  • symmetry= -X,Y-X,-Z
  • symmetry= -Y,-X,1/2-Z
  • symmetry= Y-X,Y,1/2-Z
  • symmetry= X,X-Y,1/2-Z
  • symmetry= -X,-Y,-Z
  • symmetry= Y,Y-X,-Z
  • symmetry= X-Y,X,-Z
  • symmetry= X,Y,1/2-Z
  • symmetry= Y-X,-X,1/2-Z
  • symmetry= -Y,X-Y,1/2-Z
  • symmetry= -Y,-X,Z
  • symmetry= Y-X,Y,Z
  • symmetry= X,X-Y,Z
  • symmetry= Y,X,1/2+Z
  • symmetry= X-Y,-Y,1/2+Z
  • symmetry= -X,Y-X,1/2+Z
  • asymm= 0<=x<=2/3 and 0<=y<=2/3 and 0<=z<=1/4 and x<=2 y and y<=min(1-x,2 x)
  • 195 P23

  • Number of Symmetry Operators = 12
  • Space Group Name = P23
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = 23
  • Patterson Space Group # = 200
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • asymm= 0<=x<=1 and 0<=y<=1 and 0<=z<=1/2 and y<=1-x and z<=min(x,y)
  • 196 F23

  • Number of Symmetry Operators = 48
  • Space Group Name = F23
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = 23
  • Patterson Space Group # = 202
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2+Z,X,1/2+Y
  • symmetry= 1/2+Z,-X,1/2-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= 1/2-Z,X,1/2-Y
  • symmetry= 1/2+Y,Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2-X
  • symmetry= 1/2+Y,-Z,1/2-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Z,1/2+X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,1/2-X,Y
  • symmetry= 1/2-Z,1/2+X,-Y
  • symmetry= 1/2+Y,1/2+Z,X
  • symmetry= 1/2-Y,1/2+Z,-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,1/2-Z,X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and -1/4<=z<=1/4 and y<=x and max(x-1/2,-y)<=z<=min(1/2-x,y)
  • 197 I23

  • Number of Symmetry Operators = 24
  • Space Group Name = I23
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = 23
  • Patterson Space Group # = 204
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2-X,1/2+Y
  • symmetry= 1/2-Z,1/2+X,1/2-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2-X
  • symmetry= 1/2-Y,1/2-Z,1/2+X
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1/2 and y<=min(x,1-x) and z<=y
  • 198 P2(1)3

  • Number of Symmetry Operators = 12
  • Space Group Name = P2(1)3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = 23
  • Patterson Space Group # = 200
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and -1/2<=z<=1/2 and max(x-1/2,-y)<=z<=min(x,y)
  • 199 I2(1)3

  • Number of Symmetry Operators = 24
  • Space Group Name = I2(1)3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = 23
  • Patterson Space Group # = 204
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= 1/2-X,Y,-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= Z,-X,1/2-Y
  • symmetry= -Z,1/2-X,Y
  • symmetry= 1/2-Z,X,-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,Z,-X
  • symmetry= Y,-Z,1/2-X
  • symmetry= -Y,1/2-Z,X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and z<=min(x,y)
  • 200 Pm-3

  • Number of Symmetry Operators = 24
  • Space Group Name = Pm-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 200
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and z<=min(x,y)
  • 201 Pn-3

  • Number of Symmetry Operators = 24
  • Space Group Name = Pn-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 200
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2+X,1/2-Y
  • symmetry= 1/2+Z,1/2-X,1/2+Y
  • symmetry= 1/2-Y,1/2-Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2+X
  • symmetry= 1/2+Y,1/2+Z,1/2-X
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1/2 and y<=min(x,1-x) and z<=y
  • 202 Fm-3

  • Number of Symmetry Operators = 96
  • Space Group Name = Fm-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 202
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= -X,1/2-Y,1/2-Z
  • symmetry= X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2+Z
  • symmetry= -Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2+X,1/2+Y
  • symmetry= Z,1/2+X,1/2-Y
  • symmetry= Z,1/2-X,1/2+Y
  • symmetry= -Y,1/2-Z,1/2-X
  • symmetry= Y,1/2-Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2+X
  • symmetry= Y,1/2+Z,1/2-X
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2+Z,X,1/2+Y
  • symmetry= 1/2+Z,-X,1/2-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= 1/2-Z,X,1/2-Y
  • symmetry= 1/2+Y,Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2-X
  • symmetry= 1/2+Y,-Z,1/2-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/2-X,-Y,1/2-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2+Z
  • symmetry= 1/2-Z,-X,1/2-Y
  • symmetry= 1/2-Z,X,1/2+Y
  • symmetry= 1/2+Z,X,1/2-Y
  • symmetry= 1/2+Z,-X,1/2+Y
  • symmetry= 1/2-Y,-Z,1/2-X
  • symmetry= 1/2+Y,-Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2+X
  • symmetry= 1/2+Y,Z,1/2-X
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Z,1/2+X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,1/2-X,Y
  • symmetry= 1/2-Z,1/2+X,-Y
  • symmetry= 1/2+Y,1/2+Z,X
  • symmetry= 1/2-Y,1/2+Z,-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,1/2-Z,X
  • symmetry= 1/2-X,1/2-Y,-Z
  • symmetry= 1/2+X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= 1/2-Z,1/2-X,-Y
  • symmetry= 1/2-Z,1/2+X,Y
  • symmetry= 1/2+Z,1/2+X,-Y
  • symmetry= 1/2+Z,1/2-X,Y
  • symmetry= 1/2-Y,1/2-Z,-X
  • symmetry= 1/2+Y,1/2-Z,X
  • symmetry= 1/2-Y,1/2+Z,X
  • symmetry= 1/2+Y,1/2+Z,-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4 and y<=x and z<=min(1/2-x,y)
  • 203 Fd-3

  • Number of Symmetry Operators = 96
  • Space Group Name = Fd-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 202
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/4-X,1/4-Y,1/4-Z
  • symmetry= 1/4+X,1/4+Y,1/4-Z
  • symmetry= 1/4+X,1/4-Y,1/4+Z
  • symmetry= 1/4-X,1/4+Y,1/4+Z
  • symmetry= 1/4-Z,1/4-X,1/4-Y
  • symmetry= 1/4-Z,1/4+X,1/4+Y
  • symmetry= 1/4+Z,1/4+X,1/4-Y
  • symmetry= 1/4+Z,1/4-X,1/4+Y
  • symmetry= 1/4-Y,1/4-Z,1/4-X
  • symmetry= 1/4+Y,1/4-Z,1/4+X
  • symmetry= 1/4-Y,1/4+Z,1/4+X
  • symmetry= 1/4+Y,1/4+Z,1/4-X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= 1/4-X,3/4-Y,3/4-Z
  • symmetry= 1/4+X,3/4+Y,3/4-Z
  • symmetry= 1/4+X,3/4-Y,3/4+Z
  • symmetry= 1/4-X,3/4+Y,3/4+Z
  • symmetry= 1/4-Z,3/4-X,3/4-Y
  • symmetry= 1/4-Z,3/4+X,3/4+Y
  • symmetry= 1/4+Z,3/4+X,3/4-Y
  • symmetry= 1/4+Z,3/4-X,3/4+Y
  • symmetry= 1/4-Y,3/4-Z,3/4-X
  • symmetry= 1/4+Y,3/4-Z,3/4+X
  • symmetry= 1/4-Y,3/4+Z,3/4+X
  • symmetry= 1/4+Y,3/4+Z,3/4-X
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2+Z,X,1/2+Y
  • symmetry= 1/2+Z,-X,1/2-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= 1/2-Z,X,1/2-Y
  • symmetry= 1/2+Y,Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2-X
  • symmetry= 1/2+Y,-Z,1/2-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 3/4-X,1/4-Y,3/4-Z
  • symmetry= 3/4+X,1/4+Y,3/4-Z
  • symmetry= 3/4+X,1/4-Y,3/4+Z
  • symmetry= 3/4-X,1/4+Y,3/4+Z
  • symmetry= 3/4-Z,1/4-X,3/4-Y
  • symmetry= 3/4-Z,1/4+X,3/4+Y
  • symmetry= 3/4+Z,1/4+X,3/4-Y
  • symmetry= 3/4+Z,1/4-X,3/4+Y
  • symmetry= 3/4-Y,1/4-Z,3/4-X
  • symmetry= 3/4+Y,1/4-Z,3/4+X
  • symmetry= 3/4-Y,1/4+Z,3/4+X
  • symmetry= 3/4+Y,1/4+Z,3/4-X
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Z,1/2+X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,1/2-X,Y
  • symmetry= 1/2-Z,1/2+X,-Y
  • symmetry= 1/2+Y,1/2+Z,X
  • symmetry= 1/2-Y,1/2+Z,-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,1/2-Z,X
  • symmetry= 3/4-X,3/4-Y,1/4-Z
  • symmetry= 3/4+X,3/4+Y,1/4-Z
  • symmetry= 3/4+X,3/4-Y,Z+1/4
  • symmetry= 3/4-X,3/4+Y,Z+1/4
  • symmetry= 3/4-Z,3/4-X,1/4-Y
  • symmetry= 3/4-Z,3/4+X,1/4+Y
  • symmetry= 3/4+Z,3/4+X,1/4-Y
  • symmetry= 3/4+Z,3/4-X,1/4+Y
  • symmetry= 3/4-Y,3/4-Z,1/4-X
  • symmetry= 3/4+Y,3/4-Z,1/4+X
  • symmetry= 3/4-Y,3/4+Z,1/4+X
  • symmetry= 3/4+Y,3/4+Z,1/4-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and -1/4<=z<=1/4 and y<=min(x,1/2-x) and -y<=z<=y
  • 204 Im-3

  • Number of Symmetry Operators = 48
  • Space Group Name = Im-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 204
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2-X,1/2+Y
  • symmetry= 1/2-Z,1/2+X,1/2-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2-X
  • symmetry= 1/2-Y,1/2-Z,1/2+X
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2+X,1/2-Y
  • symmetry= 1/2+Z,1/2-X,1/2+Y
  • symmetry= 1/2-Y,1/2-Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2+X
  • symmetry= 1/2+Y,1/2+Z,1/2-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=x and z<=y
  • 205 Pa-3

  • Number of Symmetry Operators = 24
  • Space Group Name = Pa-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 200
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= 1/2-Z,1/2+X,Y
  • symmetry= 1/2+Z,X,1/2-Y
  • symmetry= Z,1/2-X,1/2+Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,1/2-Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,X
  • symmetry= 1/2+Y,Z,1/2-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and z<=min(x,y)
  • 206 Ia-3

  • Number of Symmetry Operators = 48
  • Space Group Name = Ia-3
  • Crystal System = CUBIC
  • Laue Class = m-3
  • Point Group = m-3
  • Patterson Space Group # = 204
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= -X,-Y,-Z
  • symmetry= 1/2+X,Y,1/2-Z
  • symmetry= X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= 1/2-Z,1/2+X,Y
  • symmetry= 1/2+Z,X,1/2-Y
  • symmetry= Z,1/2-X,1/2+Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,1/2-Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,X
  • symmetry= 1/2+Y,Z,1/2-X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= 1/2-X,+Y,-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= Z,-X,1/2-Y
  • symmetry= -Z,1/2-X,Y
  • symmetry= 1/2-Z,X,-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,Z,-X
  • symmetry= Y,-Z,1/2-X
  • symmetry= -Y,1/2-Z,X
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= X,1/2+Y,-Z
  • symmetry= 1/2+X,-Y,Z
  • symmetry= -X,Y,1/2+Z
  • symmetry= 1/2-Z,1/2-X,1/2-Y
  • symmetry= -Z,X,1/2+Y
  • symmetry= Z,1/2+X,-Y
  • symmetry= 1/2+Z,-X,Y
  • symmetry= 1/2-Y,1/2-Z,1/2-X
  • symmetry= 1/2+Y,-Z,X
  • symmetry= -Y,Z,1/2+X
  • symmetry= Y,1/2+Z,-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4 and z<=min(x,1/2-x,1/2-y)
  • 207 P432

  • Number of Symmetry Operators = 24
  • Space Group Name = P432
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y,-X,Z
  • symmetry= -Y,X,Z
  • symmetry= X,Z,-Y
  • symmetry= -X,Z,Y
  • symmetry= -X,-Z,-Y
  • symmetry= X,-Z,Y
  • symmetry= Z,Y,-X
  • symmetry= Z,-Y,X
  • symmetry= -Z,Y,X
  • symmetry= -Z,-Y,-X
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1/2 and y<=min(x,1-x) and z<=y
  • 208 P4(2)32

  • Number of Symmetry Operators = 24
  • Space Group Name = P4(2)32
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2-Z,1/2-Y
  • symmetry= 1/2+X,1/2-Z,1/2+Y
  • symmetry= 1/2+Z,1/2+Y,1/2-X
  • symmetry= 1/2+Z,1/2-Y,1/2+X
  • symmetry= 1/2-Z,1/2+Y,1/2+X
  • symmetry= 1/2-Z,1/2-Y,1/2-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and -1/4<=z<=1/4 and max(-x,x-1/2,-y,y-1/2)<=z<=min(x,1/2-x,y,1/2-y)
  • 209 F432

  • Number of Symmetry Operators = 96
  • Space Group Name = F432
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 225
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y,-X,Z
  • symmetry= -Y,X,Z
  • symmetry= X,Z,-Y
  • symmetry= -X,Z,Y
  • symmetry= -X,-Z,-Y
  • symmetry= X,-Z,Y
  • symmetry= Z,Y,-X
  • symmetry= Z,-Y,X
  • symmetry= -Z,Y,X
  • symmetry= -Z,-Y,-X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= Y,1/2+X,1/2-Z
  • symmetry= -Y,1/2-X,1/2-Z
  • symmetry= Y,1/2-X,1/2+Z
  • symmetry= -Y,1/2+X,1/2+Z
  • symmetry= X,1/2+Z,1/2-Y
  • symmetry= -X,1/2+Z,1/2+Y
  • symmetry= -X,1/2-Z,1/2-Y
  • symmetry= X,1/2-Z,1/2+Y
  • symmetry= Z,1/2+Y,1/2-X
  • symmetry= Z,1/2-Y,1/2+X
  • symmetry= -Z,1/2+Y,1/2+X
  • symmetry= -Z,1/2-Y,1/2-X
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2+Z,X,1/2+Y
  • symmetry= 1/2+Z,-X,1/2-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= 1/2-Z,X,1/2-Y
  • symmetry= 1/2+Y,Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2-X
  • symmetry= 1/2+Y,-Z,1/2-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/2+Y,X,1/2-Z
  • symmetry= 1/2-Y,-X,1/2-Z
  • symmetry= 1/2+Y,-X,1/2+Z
  • symmetry= 1/2-Y,X,1/2+Z
  • symmetry= 1/2+X,Z,1/2-Y
  • symmetry= 1/2-X,Z,1/2+Y
  • symmetry= 1/2-X,-Z,1/2-Y
  • symmetry= 1/2+X,-Z,1/2+Y
  • symmetry= 1/2+Z,Y,1/2-X
  • symmetry= 1/2+Z,-Y,1/2+X
  • symmetry= 1/2-Z,Y,1/2+X
  • symmetry= 1/2-Z,-Y,1/2-X
  • {****}
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Z,1/2+X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,1/2-X,Y
  • symmetry= 1/2-Z,1/2+X,-Y
  • symmetry= 1/2+Y,1/2+Z,X
  • symmetry= 1/2-Y,1/2+Z,-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,1/2-Z,X
  • symmetry= 1/2+Y,1/2+X,-Z
  • symmetry= 1/2-Y,1/2-X,-Z
  • symmetry= 1/2+Y,1/2-X,Z
  • symmetry= 1/2-Y,1/2+X,Z
  • symmetry= 1/2+X,1/2+Z,-Y
  • symmetry= 1/2-X,1/2+Z,Y
  • symmetry= 1/2-X,1/2-Z,-Y
  • symmetry= 1/2+X,1/2-Z,Y
  • symmetry= 1/2+Z,1/2+Y,-X
  • symmetry= 1/2+Z,1/2-Y,X
  • symmetry= 1/2-Z,1/2+Y,X
  • symmetry= 1/2-Z,1/2-Y,-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and -1/4<=z<=1/4 and y<=min(x,1/2-x) and -y<=z<=y
  • 210 F4(1)32

  • Number of Symmetry Operators = 96
  • Space Group Name = F4(1)32
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 225
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= 1/2-Z,1/2+X,-Y
  • symmetry= Y,Z,X
  • symmetry= 1/2-Y,1/2+Z,-X
  • symmetry= 1/2+Y,-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= 3/4+Y,1/4+X,3/4-Z
  • symmetry= 1/4-Y,1/4-X,1/4-Z
  • symmetry= 1/4+Y,3/4-X,3/4+Z
  • symmetry= 3/4-Y,3/4+X,1/4+Z
  • {* << *}
  • symmetry= 3/4+X,1/4+Z,3/4-Y
  • symmetry= 3/4-X,3/4+Z,1/4+Y
  • symmetry= 1/4-X,1/4-Z,1/4-Y
  • symmetry= 1/4+X,3/4-Z,3/4+Y
  • symmetry= 3/4+Z,1/4+Y,3/4-X
  • symmetry= 1/4+Z,3/4-Y,3/4+X
  • symmetry= 3/4-Z,3/4+Y,1/4+X
  • symmetry= 1/4-Z,1/4-Y,1/4-X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,-Y,Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= 1/2-Z,X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 3/4+Y,3/4+X,1/4-Z
  • symmetry= 1/4-Y,3/4-X,3/4-Z
  • symmetry= 1/4+Y,1/4-X,1/4+Z
  • symmetry= 3/4-Y,1/4+X,3/4+Z
  • {* << *}
  • symmetry= 3/4+X,3/4+Z,1/4-Y
  • symmetry= 3/4-X,1/4+Z,3/4+Y
  • symmetry= 1/4-X,3/4-Z,3/4-Y
  • symmetry= 1/4+X,1/4-Z,1/4+Y
  • symmetry= 3/4+Z,3/4+Y,1/4-X
  • symmetry= 1/4+Z,1/4-Y,1/4+X
  • symmetry= 3/4-Z,1/4+Y,3/4+X
  • symmetry= 1/4-Z,3/4-Y,3/4-X
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,-Y,-Z
  • symmetry= 1/2+Z,X,1/2+Y
  • symmetry= Z,-X,-Y
  • symmetry= 1/2-Z,1/2-X,Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= 1/2+Y,Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,-Z,-X
  • symmetry= 1/2-Y,1/2-Z,X
  • symmetry= 1/4+Y,1/4+X,1/4-Z
  • symmetry= 3/4-Y,1/4-X,3/4-Z
  • symmetry= 3/4+Y,3/4-X,1/4+Z
  • symmetry= 1/4-Y,3/4+X,3/4+Z
  • {* << *}
  • symmetry= 1/4+X,1/4+Z,1/4-Y
  • symmetry= 1/4-X,3/4+Z,3/4+Y
  • symmetry= 3/4-X,1/4-Z,3/4-Y
  • symmetry= 3/4+X,3/4-Z,1/4+Y
  • symmetry= 1/4+Z,1/4+Y,1/4-X
  • symmetry= 3/4+Z,3/4-Y,1/4+X
  • symmetry= 1/4-Z,3/4+Y,3/4+X
  • symmetry= 3/4-Z,1/4-Y,3/4-X
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,Y,-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,X,-Y
  • symmetry= 1/2+Y,1/2+Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/4+Y,3/4+X,3/4-Z
  • symmetry= 3/4-Y,3/4-X,1/4-Z
  • symmetry= 3/4+Y,1/4-X,3/4+Z
  • symmetry= 1/4-Y,1/4+X,1/4+Z
  • {* << *}
  • symmetry= 1/4+X,3/4+Z,3/4-Y
  • symmetry= 1/4-X,1/4+Z,1/4+Y
  • symmetry= 3/4-X,3/4-Z,1/4-Y
  • symmetry= 3/4+X,1/4-Z,3/4+Y
  • symmetry= 1/4+Z,3/4+Y,3/4-X
  • symmetry= 3/4+Z,1/4-Y,3/4+X
  • symmetry= 1/4-Z,1/4+Y,1/4+X
  • symmetry= 3/4-Z,3/4-Y,1/4-X
  • asymm= 0<=x<=1/2 and -1/8<=y<=1/8 and -1/8<=z<=1/8 and y<=min(x,1/2-x) and -y<=z<=min(x,1/2-x)
  • 211 I432

  • Number of Symmetry Operators = 48
  • Space Group Name = I432
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 229
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y,-X,Z
  • symmetry= -Y,X,Z
  • symmetry= X,Z,-Y
  • symmetry= -X,Z,Y
  • symmetry= -X,-Z,-Y
  • symmetry= X,-Z,Y
  • symmetry= Z,Y,-X
  • symmetry= Z,-Y,X
  • symmetry= -Z,Y,X
  • symmetry= -Z,-Y,-X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2-X,1/2+Y
  • symmetry= 1/2-Z,1/2+X,1/2-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2-X
  • symmetry= 1/2-Y,1/2-Z,1/2+X
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2-Z,1/2-Y
  • symmetry= 1/2+X,1/2-Z,1/2+Y
  • symmetry= 1/2+Z,1/2+Y,1/2-X
  • symmetry= 1/2+Z,1/2-Y,1/2+X
  • symmetry= 1/2-Z,1/2+Y,1/2+X
  • symmetry= 1/2-Z,1/2-Y,1/2-X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4 and z<=min(x,1/2-x,y,1/2-y)
  • 212 P4(3)32

  • Number of Symmetry Operators = 24
  • Space Group Name = P4(3)32
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/4+Y,3/4+X,3/4-Z
  • symmetry= 1/4-Y,1/4-X,1/4-Z
  • symmetry= 3/4+Y,3/4-X,1/4+Z
  • symmetry= 3/4-Y,1/4+X,3/4+Z
  • symmetry= 1/4+X,3/4+Z,3/4-Y
  • symmetry= 3/4-X,1/4+Z,3/4+Y
  • symmetry= 1/4-X,1/4-Z,1/4-Y
  • symmetry= 3/4+X,3/4-Z,1/4+Y
  • symmetry= 1/4+Z,3/4+Y,3/4-X
  • symmetry= 3/4+Z,3/4-Y,1/4+X
  • symmetry= 3/4-Z,1/4+Y,3/4+X
  • symmetry= 1/4-Z,1/4-Y,1/4-X
  • asymm= 0<=x<=1/2 and 0<=y<=3/4 and -1/2<=z<=1/4 and max(-y,x-1/2)<=z<=min(1/2-y,2 x-y,2 y-x,y-2 x+1/2)
  • 213 P4(1)32

  • Number of Symmetry Operators = 24
  • Space Group Name = P4(1)32
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 3/4+Y,1/4+X,1/4-Z
  • symmetry= 3/4-Y,3/4-X,3/4-Z
  • symmetry= 1/4+Y,1/4-X,3/4+Z
  • symmetry= 1/4-Y,3/4+X,1/4+Z
  • symmetry= 3/4+X,1/4+Z,1/4-Y
  • symmetry= 1/4-X,3/4+Z,1/4+Y
  • symmetry= 3/4-X,3/4-Z,3/4-Y
  • symmetry= 1/4+X,1/4-Z,3/4+Y
  • symmetry= 3/4+Z,1/4+Y,1/4-X
  • symmetry= 1/4+Z,1/4-Y,3/4+X
  • symmetry= 1/4-Z,3/4+Y,1/4+X
  • symmetry= 3/4-Z,3/4-Y,3/4-X
  • asymm= -1/4<=x<=1/2 and 0<=y<=3/4 and 0<=z<=1/2 and x<=y<=x+1/2 and
  • y-x)/2<=z<=min(y,(-4 x-2 y+3)/2,(3-2 x-2 y)/4)
  • 214 I4(1)32

  • Number of Symmetry Operators = 48
  • Space Group Name = I4(1)32
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = 432
  • Patterson Space Group # = 229
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 3/4+Y,1/4+X,1/4-Z
  • symmetry= 3/4-Y,3/4-X,3/4-Z
  • symmetry= 1/4+Y,1/4-X,3/4+Z
  • symmetry= 1/4-Y,3/4+X,1/4+Z
  • symmetry= 3/4+X,1/4+Z,1/4-Y
  • symmetry= 1/4-X,3/4+Z,1/4+Y
  • symmetry= 3/4-X,3/4-Z,3/4-Y
  • symmetry= 1/4+X,1/4-Z,3/4+Y
  • symmetry= 3/4+Z,1/4+Y,1/4-X
  • symmetry= 1/4+Z,1/4-Y,3/4+X
  • symmetry= 1/4-Z,3/4+Y,1/4+X
  • symmetry= 3/4-Z,3/4-Y,3/4-X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,Z
  • symmetry= 1/2-X,Y,-Z
  • symmetry= X,-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= Z,-X,1/2-Y
  • symmetry= -Z,1/2-X,Y
  • symmetry= 1/2-Z,X,-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,Z,-X
  • symmetry= Y,-Z,1/2-X
  • symmetry= -Y,1/2-Z,X
  • symmetry= 1/4+Y,3/4+X,3/4-Z
  • symmetry= 1/4-Y,1/4-X,1/4-Z
  • symmetry= 3/4+Y,3/4-X,1/4+Z
  • symmetry= 3/4-Y,1/4+X,3/4+Z
  • symmetry= 1/4+X,3/4+Z,3/4-Y
  • symmetry= 3/4-X,1/4+Z,3/4+Y
  • symmetry= 1/4-X,1/4-Z,1/4-Y
  • symmetry= 3/4+X,3/4-Z,1/4+Y
  • symmetry= 1/4+Z,3/4+Y,3/4-X
  • symmetry= 3/4+Z,3/4-Y,1/4+X
  • symmetry= 3/4-Z,1/4+Y,3/4+X
  • symmetry= 1/4-Z,1/4-Y,1/4-X
  • asymm= -3/8<=x<=1/8 and -1/8<=y<=1/8 and -1/8<=z<=3/8 and max(x,y,y-x-1/8)<=z<=y+1/4
  • 215 P-43m

  • Number of Symmetry Operators = 24
  • Space Group Name = P-43m
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = -43m
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= Z,Y,X
  • symmetry= Z,-Y,-X
  • symmetry= -Z,Y,-X
  • symmetry= -Z,-Y,X
  • asymm= 0<=x<=1 and 0<=y<=1/2 and 0<=z<=1/2 and y<=min(x,1-x) and z<=y
  • 216 F4-3m

  • Number of Symmetry Operators = 96
  • Space Group Name = F4-3m
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = -43m
  • Patterson Space Group # = 225
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= Z,Y,X
  • symmetry= Z,-Y,-X
  • symmetry= -Z,Y,-X
  • symmetry= -Z,-Y,X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= Y,1/2+X,1/2+Z
  • symmetry= -Y,1/2-X,1/2+Z
  • symmetry= Y,1/2-X,1/2-Z
  • symmetry= -Y,1/2+X,1/2-Z
  • symmetry= X,1/2+Z,1/2+Y
  • symmetry= -X,1/2+Z,1/2-Y
  • symmetry= -X,1/2-Z,1/2+Y
  • symmetry= X,1/2-Z,1/2-Y
  • symmetry= Z,1/2+Y,1/2+X
  • symmetry= Z,1/2-Y,1/2-X
  • symmetry= -Z,1/2+Y,1/2-X
  • symmetry= -Z,1/2-Y,1/2+X
  • symmetry= 1/2+X,Y,1/2+Z
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= 1/2-X,Y,1/2-Z
  • symmetry= 1/2+X,-Y,1/2-Z
  • symmetry= 1/2+Z,X,1/2+Y
  • symmetry= 1/2+Z,-X,1/2-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= 1/2-Z,X,1/2-Y
  • symmetry= 1/2+Y,Z,1/2+X
  • symmetry= 1/2-Y,Z,1/2-X
  • symmetry= 1/2+Y,-Z,1/2-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/2+Y,X,1/2+Z
  • symmetry= 1/2-Y,-X,1/2+Z
  • symmetry= 1/2+Y,-X,1/2-Z
  • symmetry= 1/2-Y,X,1/2-Z
  • symmetry= 1/2+X,Z,1/2+Y
  • symmetry= 1/2-X,Z,1/2-Y
  • symmetry= 1/2-X,-Z,1/2+Y
  • symmetry= 1/2+X,-Z,1/2-Y
  • symmetry= 1/2+Z,Y,1/2+X
  • symmetry= 1/2+Z,-Y,1/2-X
  • symmetry= 1/2-Z,Y,1/2-X
  • symmetry= 1/2-Z,-Y,1/2+X
  • symmetry= 1/2+X,1/2+Y,Z
  • symmetry= 1/2-X,1/2-Y,Z
  • symmetry= 1/2-X,1/2+Y,-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= 1/2+Z,1/2+X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,1/2-X,Y
  • symmetry= 1/2-Z,1/2+X,-Y
  • symmetry= 1/2+Y,1/2+Z,X
  • symmetry= 1/2-Y,1/2+Z,-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,1/2-Z,X
  • symmetry= 1/2+Y,1/2+X,Z
  • symmetry= 1/2-Y,1/2-X,Z
  • symmetry= 1/2+Y,1/2-X,-Z
  • symmetry= 1/2-Y,1/2+X,-Z
  • symmetry= 1/2+X,1/2+Z,Y
  • symmetry= 1/2-X,1/2+Z,-Y
  • symmetry= 1/2-X,1/2-Z,Y
  • symmetry= 1/2+X,1/2-Z,-Y
  • symmetry= 1/2+Z,1/2+Y,X
  • symmetry= 1/2+Z,1/2-Y,-X
  • symmetry= 1/2-Z,1/2+Y,-X
  • symmetry= 1/2-Z,1/2-Y,X
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and -1/4<=z<=1/4 and y<=min(x,1/2-x) and -y<=z<=y
  • 217 I-43m

  • Number of Symmetry Operators = 48
  • Space Group Name = I-43m
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = -43m
  • Patterson Space Group # = 229
  • Lattice Type = I
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,Z
  • symmetry= -Y,-X,Z
  • symmetry= Y,-X,-Z
  • symmetry= -Y,X,-Z
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= Z,Y,X
  • symmetry= Z,-Y,-X
  • symmetry= -Z,Y,-X
  • symmetry= -Z,-Y,X
  • symmetry= 1/2+X,1/2+Y,1/2+Z
  • symmetry= 1/2-X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2-Z
  • symmetry= 1/2+Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2-X,1/2+Y
  • symmetry= 1/2-Z,1/2+X,1/2-Y
  • symmetry= 1/2+Y,1/2+Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2-X
  • symmetry= 1/2-Y,1/2-Z,1/2+X
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2-Z,1/2+Y
  • symmetry= 1/2+X,1/2-Z,1/2-Y
  • symmetry= 1/2+Z,1/2+Y,1/2+X
  • symmetry= 1/2+Z,1/2-Y,1/2-X
  • symmetry= 1/2-Z,1/2+Y,1/2-X
  • symmetry= 1/2-Z,1/2-Y,1/2+X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=x and z<=y
  • 218 P-43n

  • Number of Symmetry Operators = 24
  • Space Group Name = P-43n
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = -43m
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2-Z,1/2+Y
  • symmetry= 1/2+X,1/2-Z,1/2-Y
  • symmetry= 1/2+Z,1/2+Y,1/2+X
  • symmetry= 1/2+Z,1/2-Y,1/2-X
  • symmetry= 1/2-Z,1/2+Y,1/2-X
  • symmetry= 1/2-Z,1/2-Y,1/2+X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and z<=min(x,y)
  • 219 F-43c

  • Number of Symmetry Operators = 96
  • Space Group Name = F-43c
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = -43m
  • Patterson Space Group # = 225
  • Lattice Type = F
  • symmetry= X,Y,Z
  • {***}
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2-Z,1/2+Y
  • symmetry= 1/2+X,1/2-Z,1/2-Y
  • symmetry= 1/2+Z,1/2+Y,1/2+X
  • symmetry= 1/2+Z,1/2-Y,1/2-X
  • symmetry= 1/2-Z,1/2+Y,1/2-X
  • symmetry= 1/2-Z,1/2-Y,1/2+X
  • symmetry= X,Y+1/2,Z+1/2
  • {***}
  • symmetry= -X,-Y+1/2,Z+1/2
  • symmetry= -X,Y+1/2,-Z+1/2
  • symmetry= X,-Y+1/2,-Z+1/2
  • symmetry= Z,X+1/2,Y+1/2
  • symmetry= Z,-X+1/2,-Y+1/2
  • symmetry= -Z,-X+1/2,Y+1/2
  • symmetry= -Z,X+1/2,-Y+1/2
  • symmetry= Y,Z+1/2,X+1/2
  • symmetry= -Y,Z+1/2,-X+1/2
  • symmetry= Y,-Z+1/2,-X+1/2)
  • symmetry= -Y,-Z+1/2,X+1/2
  • symmetry= 1/2+Y,X,Z
  • symmetry= 1/2-Y,-X,Z
  • symmetry= 1/2+Y,-X,-Z
  • symmetry= 1/2-Y,+X,-Z
  • symmetry= 1/2+X,+Z,Y
  • symmetry= 1/2-X,+Z,-Y
  • symmetry= 1/2-X,-Z,Y
  • symmetry= 1/2+X,-Z,-Y
  • symmetry= 1/2+Z,+Y,X
  • symmetry= 1/2+Z,-Y,-X
  • symmetry= 1/2-Z,+Y,-X
  • symmetry= 1/2-Z,-Y,X
  • symmetry= X+1/2,Y,Z+1/2
  • {***}
  • symmetry= -X+1/2,-Y,Z+1/2
  • symmetry= -X+1/2,Y,-Z+1/2
  • symmetry= X+1/2,-Y,-Z+1/2
  • symmetry= Z+1/2,X,Y+1/2
  • symmetry= Z+1/2,-X,-Y+1/2
  • symmetry= -Z+1/2,-X,Y+1/2
  • symmetry= -Z+1/2,X,-Y+1/2
  • symmetry= Y+1/2,Z,X+1/2
  • symmetry= -Y+1/2,Z,-X+1/2
  • symmetry= Y+1/2,-Z,-X+1/2
  • symmetry= -Y+1/2,-Z,X+1/2
  • symmetry= Y,1/2+X,Z
  • symmetry= -Y,1/2-X,Z
  • symmetry= Y,1/2-X,-Z
  • symmetry= -Y,1/2+X,-Z
  • symmetry= X,1/2+Z,Y
  • symmetry=(-X,1/2+Z,-Y
  • symmetry= -X,1/2-Z,Y
  • symmetry= X,1/2-Z,-Y
  • symmetry= Z,1/2+Y,X
  • symmetry= Z,1/2-Y,-X
  • symmetry= -Z,1/2+Y,-X
  • symmetry= -Z,1/2-Y,X
  • symmetry= X+1/2,Y+1/2,Z
  • {***}
  • symmetry= -X+1/2,-Y+1/2,Z
  • symmetry= -X+1/2,Y+1/2,-Z
  • symmetry= X+1/2,-Y+1/2,-Z
  • symmetry= Z+1/2,X+1/2,Y
  • symmetry= Z+1/2,-X+1/2,-Y
  • symmetry= -Z+1/2,-X+1/2,Y
  • symmetry= -Z+1/2,X+1/2,-Y
  • symmetry= Y+1/2,Z+1/2,X
  • symmetry= -Y+1/2,Z+1/2,-X
  • symmetry= Y+1/2,-Z+1/2,-X
  • symmetry= -Y+1/2,-Z+1/2,X
  • symmetry= Y,X,1/2+Z
  • symmetry= -Y,-X,1/2+Z
  • symmetry= Y,-X,1/2-Z
  • symmetry= -Y,X,1/2-Z
  • symmetry= X,Z,1/2+Y
  • symmetry= -X,Z,1/2-Y
  • symmetry= -X,-Z,1/2+Y
  • symmetry= X,-Z,1/2-Y
  • symmetry= Z,Y,1/2+X
  • symmetry= Z,-Y,1/2-X
  • symmetry= -Z,Y,1/2-X
  • symmetry= -Z,-Y,1/2+X
  • asymm= 0<=x<=1/2 and 0<=y<=1/4 and -1/4<=z<=1/4 and y<=min(x,1/2-x) and -y<=z<=y
  • 220 I-43d

  • Number of Symmetry Operators = 48
  • Space Group Name = I-43d
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = -43m
  • Patterson Space Group # = 229
  • Lattice Type = I
  • symmetry= X,Y,Z
  • {***}
  • symmetry= 1/2-X,-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= 1/2+Z,1/2-X,-Y
  • symmetry= 1/2-Z,-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,-X
  • symmetry= 1/2-Y,-Z,1/2+X
  • symmetry= 1/4+Y,1/4+X,1/4+Z
  • symmetry= 1/4-Y,3/4-X,3/4+Z
  • symmetry= 3/4+Y,1/4-X,3/4-Z
  • symmetry= 3/4-Y,3/4+X,1/4-Z
  • symmetry= 1/4+X,1/4+Z,1/4+Y
  • symmetry= 3/4-X,3/4+Z,1/4-Y
  • symmetry= 1/4-X,3/4-Z,3/4+Y
  • symmetry= 3/4+X,1/4-Z,3/4-Y
  • symmetry= 1/4+Z,1/4+Y,1/4+X
  • symmetry= 3/4+Z,1/4-Y,3/4-X
  • symmetry= 3/4-Z,3/4+Y,1/4-X
  • symmetry= 1/4-Z,3/4-Y,3/4+X
  • symmetry= X+1/2,Y+1/2,Z+1/2
  • {***}
  • symmetry= -X,-Y+1/2,Z
  • symmetry= -X+1/2,Y,-Z
  • symmetry= X,-Y,-Z+1/2
  • symmetry= Z+1/2,X+1/2,Y+1/2
  • symmetry= Z,-X,-Y+1/2
  • symmetry= -Z,-X+1/2,Y
  • symmetry= -Z+1/2,X,-Y
  • symmetry= Y+1/2,Z+1/2,X+1/2
  • symmetry= -Y+1/2,Z,-X
  • symmetry= Y,-Z,-X+1/2
  • symmetry= -Y,-Z+1/2,X
  • symmetry= 3/4+Y,3/4+X,3/4+Z
  • symmetry= 3/4-Y,1/4-X,1/4+Z
  • symmetry= 1/4+Y,3/4-X,1/4-Z
  • symmetry= 1/4-Y,1/4+X,3/4-Z
  • symmetry= 3/4+X,3/4+Z,3/4+Y
  • symmetry= 1/4-X,1/4+Z,3/4-Y
  • symmetry= 3/4-X,1/4-Z,1/4+Y
  • symmetry= 1/4+X,3/4-Z,1/4-Y
  • symmetry= 3/4+Z,3/4+Y,3/4+X
  • symmetry= 1/4+Z,3/4-Y,1/4-X
  • symmetry= 1/4-Z,1/4+Y,3/4-X
  • symmetry= 3/4-Z,1/4-Y,1/4+X
  • asymm= 1/4<=x<=1/2 and 1/4<=y<=1/2 and 0<=z<=1/2 and z<=min(x,y)
  • 221 Pm-3m

  • Number of Symmetry Operators = 48
  • Space Group Name = Pm-3m
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = m-3m
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y,-X,Z
  • symmetry= -Y,X,Z
  • symmetry= X,Z,-Y
  • symmetry= -X,Z,Y
  • symmetry= -X,-Z,-Y
  • symmetry= X,-Z,Y
  • symmetry= Z,Y,-X
  • symmetry= Z,-Y,X
  • symmetry= -Z,Y,X
  • symmetry= -Z,-Y,-X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -Z,-Y,X
  • symmetry= -Z,Y,-X
  • symmetry= Z,-Y,-X
  • symmetry= Z,Y,X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=x and z<=y
  • 222 Pn-3n

  • Number of Symmetry Operators = 48
  • Space Group Name = Pn-3n
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = m-3m
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y,-X,Z
  • symmetry= -Y,X,Z
  • symmetry= X,Z,-Y
  • symmetry= -X,Z,Y
  • symmetry= -X,-Z,-Y
  • symmetry= X,-Z,Y
  • symmetry= Z,Y,-X
  • symmetry= Z,-Y,X
  • symmetry= -Z,Y,X
  • symmetry= -Z,-Y,-X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -Z,-Y,X
  • symmetry= -Z,Y,-X
  • symmetry= Z,-Y,-X
  • symmetry= Z,Y,X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/2 and y<=x and z<=y
  • 223 Pm-3n

  • Number of Symmetry Operators = 48
  • Space Group Name = Pm-3n
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = m-3m
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2-Z,1/2-Y
  • symmetry= 1/2+X,1/2-Z,1/2+Y
  • symmetry= 1/2+Z,1/2+Y,1/2-X
  • symmetry= 1/2+Z,1/2-Y,1/2+X
  • symmetry= 1/2-Z,1/2+Y,1/2+X
  • symmetry= 1/2-Z,1/2-Y,1/2-X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • symmetry= 1/2-Y,1/2-X,1/2+Z
  • symmetry= 1/2+Y,1/2+X,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2-Z
  • symmetry= 1/2-X,1/2-Z,1/2+Y
  • symmetry= 1/2+X,1/2-Z,1/2-Y
  • symmetry= 1/2+X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2+Z,1/2-Y
  • symmetry= 1/2-Z,1/2-Y,1/2+X
  • symmetry= 1/2-Z,1/2+Y,1/2-X
  • symmetry= 1/2+Z,1/2-Y,1/2-X
  • symmetry= 1/2+Z,1/2+Y,1/2+X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and 0<=z<=1/4 and z<=min(x,1/2-x,y,1/2-y)
  • 224 Pn-3m

  • Number of Symmetry Operators = 48
  • Space Group Name = Pn-3m
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = m-3m
  • Patterson Space Group # = 221
  • Lattice Type = P
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= 1/2+Y,1/2+X,1/2-Z
  • symmetry= 1/2-Y,1/2-X,1/2-Z
  • symmetry= 1/2+Y,1/2-X,1/2+Z
  • symmetry= 1/2-Y,1/2+X,1/2+Z
  • symmetry= 1/2+X,1/2+Z,1/2-Y
  • symmetry= 1/2-X,1/2+Z,1/2+Y
  • symmetry= 1/2-X,1/2-Z,1/2-Y
  • symmetry= 1/2+X,1/2-Z,1/2+Y
  • symmetry= 1/2+Z,1/2+Y,1/2-X
  • symmetry= 1/2+Z,1/2-Y,1/2+X
  • symmetry= 1/2-Z,1/2+Y,1/2+X
  • symmetry= 1/2-Z,1/2-Y,1/2-X
  • symmetry= 1/2-X,1/2-Y,1/2-Z
  • symmetry= 1/2+X,1/2+Y,1/2-Z
  • symmetry= 1/2+X,1/2-Y,1/2+Z
  • symmetry= 1/2-X,1/2+Y,1/2+Z
  • symmetry= 1/2-Z,1/2-X,1/2-Y
  • symmetry= 1/2-Z,1/2+X,1/2+Y
  • symmetry= 1/2+Z,1/2+X,1/2-Y
  • symmetry= 1/2+Z,1/2-X,1/2+Y
  • symmetry= 1/2-Y,1/2-Z,1/2-X
  • symmetry= 1/2+Y,1/2-Z,1/2+X
  • symmetry= 1/2-Y,1/2+Z,1/2+X
  • symmetry= 1/2+Y,1/2+Z,1/2-X
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -Z,-Y,X
  • symmetry= -Z,Y,-X
  • symmetry= Z,-Y,-X
  • symmetry= Z,Y,X
  • asymm= 0<=x<=1/2 and 0<=y<=1/2 and -1/4<=z<=1/4 and y<=x and max(x-1/2,-y)<=z<=min(1/2-x,y)
  • 225 Fm-3m

  • Number of Symmetry Operators = 192
  • Space Group Name = Fm-3m
  • Crystal System = CUBIC
  • Laue Class = m-3m
  • Point Group = m-3m
  • Patterson Space Group # = 225
  • Lattice Type = F
  • symmetry= X,Y,Z
  • symmetry= -X,-Y,Z
  • symmetry= -X,Y,-Z
  • symmetry= X,-Y,-Z
  • symmetry= Z,X,Y
  • symmetry= Z,-X,-Y
  • symmetry= -Z,-X,Y
  • symmetry= -Z,X,-Y
  • symmetry= Y,Z,X
  • symmetry= -Y,Z,-X
  • symmetry= Y,-Z,-X
  • symmetry= -Y,-Z,X
  • symmetry= Y,X,-Z
  • symmetry= -Y,-X,-Z
  • symmetry= Y,-X,Z
  • symmetry= -Y,X,Z
  • symmetry= X,Z,-Y
  • symmetry= -X,Z,Y
  • symmetry= -X,-Z,-Y
  • symmetry= X,-Z,Y
  • symmetry= Z,Y,-X
  • symmetry= Z,-Y,X
  • symmetry= -Z,Y,X
  • symmetry= -Z,-Y,-X
  • symmetry= -X,-Y,-Z
  • symmetry= X,Y,-Z
  • symmetry= X,-Y,Z
  • symmetry= -X,Y,Z
  • symmetry= -Z,-X,-Y
  • symmetry= -Z,X,Y
  • symmetry= Z,X,-Y
  • symmetry= Z,-X,Y
  • symmetry= -Y,-Z,-X
  • symmetry= Y,-Z,X
  • symmetry= -Y,Z,X
  • symmetry= Y,Z,-X
  • symmetry= -Y,-X,Z
  • symmetry= Y,X,Z
  • symmetry= -Y,X,-Z
  • symmetry= Y,-X,-Z
  • symmetry= -X,-Z,Y
  • symmetry= X,-Z,-Y
  • symmetry= X,Z,Y
  • symmetry= -X,Z,-Y
  • symmetry= -Z,-Y,X
  • symmetry= -Z,Y,-X
  • symmetry= Z,-Y,-X
  • symmetry= Z,Y,X
  • symmetry= X,1/2+Y,1/2+Z
  • symmetry= -X,1/2-Y,1/2+Z
  • symmetry= -X,1/2+Y,1/2-Z
  • symmetry= X,1/2-Y,1/2-Z
  • symmetry= Z,1/2+X,1/2+Y
  • symmetry= Z,1/2-X,1/2-Y
  • symmetry= -Z,1/2-X,1/2+Y
  • symmetry= -Z,1/2+X,1/2-Y
  • symmetry= Y,1/2+Z,1/2+X
  • symmetry= -Y,1/2+Z,1/2-X
  • symmetry= Y,1/2-Z,1/2-X
  • symmetry= -Y,1/2-Z,1/2+X
  • symmetry= Y,1/2+X,1/2-Z
  • symmetry= -Y,1/2-X,1/2-Z
  • symmetry= Y,1/2-X,1/2+Z
  • symmetry= -Y,1/2+X,1/2+Z
  • symmetry= X,1/2+Z,1/2-Y
  • symmetry= -X,1/2+Z,1/2+Y
  • symmetry= -X,1/2-Z,1/2-Y
  • symmetry= X,1/2-Z,1/2+Y
  • symmetry= Z,1/2+Y,1/2-X
  • symmetry= Z,1/2-Y,1/2+X
  • symmetry= -Z,1/2+Y,1/2+X
  • symmetry= -Z,1/2-Y,1/2-X
  • symmetry= -X,1/2-Y,1/2-Z
  • symme