Table of Space Groups in 3 Dimensions
| # | Crystal system | Point group | Space groups (international short symbol) | |
|---|---|---|---|---|
| Intl | Schönflies | |||
| 1 | Triclinic (2) | 1 | C1 Chiral | P1 |
| 2 | 1 | Ci | P1 | |
| 3–5 | Monoclinic (13) | 2 | C2 Chiral | P2, P21, C2 |
| 6–9 | m | Cs | Pm, Pc, Cm, Cc | |
| 10–15 | 2/m | C2h | P2/m, P21/m, C2/m, P2/c, P21/c, C2/c | |
| 16–24 | Orthorhombic (59) | 222 | D2 Chiral | P222, P2221, P21212, P212121, C2221, C222, F222, I222, I212121 |
| 25–46 | mm2 | C2v | Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2, Cmm2, Cmc21, Ccc2, Amm2, Aem2, Ama2, Aea2, Fmm2, Fdd2, Imm2, Iba2, Ima2 | |
| 47–74 | mmm | D2h | Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma, Cmcm, Cmce, Cmmm, Cccm, Cmme, Ccce, Fmmm, Fddd, Immm, Ibam, Ibca, Imma | |
| 75–80 | Tetragonal (68) | 4 | C4 Chiral | P4, P41, P42, P43, I4, I41 |
| 81–82 | 4 | S4 | P4, I4 | |
| 83–88 | 4/m | C4h | P4/m, P42/m, P4/n, P42/n, I4/m, I41/a | |
| 89–98 | 422 | D4 Chiral | P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212, I422, I4122 | |
| 99–110 | 4mm | C4v | P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc, I4mm, I4cm, I41md, I41cd | |
| 111–122 | 42m | D2d | P42m, P42c, P421m, P421c, P4m2, P4c2, P4b2, P4n2, I4m2, I4c2, I42m, I42d | |
| 123–142 | 4/mmm | D4h | P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P42/mmc, P42/mcm, P42/nbc, P42/nnm, P42/mbc, P42/mnm, P42/nmc, P42/ncm, I4/mmm, I4/mcm, I41/amd, I41/acd | |
| 143–146 | Trigonal (25) | 3 | C3 Chiral | P3, P31, P32, R3 |
| 147–148 | 3 | S6 | P3, R3 | |
| 149–155 | 32 | D3 Chiral | P312, P321, P3112, P3121, P3212, P3221, R32 | |
| 156–161 | 3m | C3v | P3m1, P31m, P3c1, P31c, R3m, R3c | |
| 162–167 | 3m | D3d | P31m, P31c, P3m1, P3c1, R3m, R3c, | |
| 168–173 | Hexagonal (27) | 6 | C6 Chiral | P6, P61, P65, P62, P64, P63 |
| 174 | 6 | C3h | P6 | |
| 175–176 | 6/m | C6h | P6/m, P63/m | |
| 177–182 | 622 | D6 Chiral | P622, P6122, P6522, P6222, P6422, P6322 | |
| 183–186 | 6mm | C6v | P6mm, P6cc, P63cm, P63mc | |
| 187–190 | 6m2 | D3h | P6m2, P6c2, P62m, P62c | |
| 191–194 | 6/mmm | D6h | P6/mmm, P6/mcc, P63/mcm, P63/mmc | |
| 195–199 | Cubic (36) | 23 | T Chiral | P23, F23, I23, P213, I213 |
| 200–206 | m3 | Th | Pm3, Pn3, Fm3, Fd3, Im3, Pa3, Ia3 | |
| 207–214 | 432 | O Chiral | P432, P4232, F432, F4132, I432, P4332, P4132, I4132 | |
| 215–220 | 43m | Td | P43m, F43m, I43m, P43n, F43c, I43d | |
| 221–230 | m3m | Oh | Pm3m, Pn3n, Pm3n, Pn3m, Fm3m, Fm3c, Fd3m, Fd3c, Im3m, Ia3d | |
Note. An e plane is a double glide plane, one having glides in two different directions. They are found in seven orthorombic, five tetragonal and five cubic space groups, all with centered lattice. The use of the symbol e became official with Hahn (2002).
The lattice system can be found as follows. If the crystal system is not trigonal then the lattice system is of the same type. If the crystal system is trigonal, then the lattice system is hexagonal unless the space group is one of the seven in the rhombohedral lattice system consisting of the 7 trigonal space groups in the table above whose name begins with R. (The term rhombohedral system is also sometimes used as an alternative name for the whole trigonal system.) The hexagonal lattice system is larger than the hexagonal crystal system, and consists of the hexagonal crystal system together with the 18 groups of the trigonal crystal system other than the seven whose names begin with R.
The Bravais lattice of the space group is determined by the lattice system together with the initial letter of its name, which for the non-rhombohedral groups is P, I, F, or C, standing for the principal, body centered, face centered, or C-face centered lattices.
Read more about this topic: Space Group
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