Crystal Lab › The 75 rod groups
The 75 rod groups
3D objects periodic in one direction. Open a group to see its symmetry elements drawn in the cell, its operations, and its Wyckoff positions with a model atom you can move.
The 230 space groups · The 17 plane groups · The 7 frieze groups · The 75 rod groups · The 80 layer groups
Monoclinic (10)
Orthorhombic (10)
Tetragonal (19)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 23 | p 4 | 4 | 2 | 1 |
| 24 | p4₁ | 4 | 1 | 1 |
| 25 | p4₂ | 4 | 2 | 1 |
| 26 | p4₃ | 4 | 1 | 1 |
| 27 | p4̅ | 4 | 4 | 1 |
| 28 | p 4/m | 8 | 6 | 1 |
| 29 | p4₂/m | 8 | 5 | 1 |
| 30 | p422 | 8 | 8 | 1 |
| 31 | p4₁22 | 8 | 3 | 1 |
| 32 | p4₂22 | 8 | 8 | 1 |
| 33 | p4₃22 | 8 | 3 | 1 |
| 34 | p4mm | 8 | 4 | 1 |
| 35 | p4₂cm, origin 1 | 8 | 3 | 2 |
| 36 | p4cc | 8 | 2 | 1 |
| 37 | p4̅2m, origin 1 | 8 | 7 | 2 |
| 38 | p4̅2c, origin 1 | 8 | 6 | 2 |
| 39 | p4/mmm | 16 | 12 | 1 |
| 40 | p4/mcc | 16 | 7 | 1 |
| 41 | p4₂/mmc, origin 1 | 16 | 9 | 2 |
Trigonal (11)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 42 | p 3 | 3 | 2 | 1 |
| 43 | p3₁ | 3 | 1 | 1 |
| 44 | p3₂ | 3 | 1 | 1 |
| 45 | p3̅ | 6 | 4 | 1 |
| 46 | p312, origin 1 | 6 | 6 | 2 |
| 47 | p3₁12, origin 1 | 6 | 3 | 2 |
| 48 | p3₂12, origin 1 | 6 | 3 | 2 |
| 49 | p3m1, origin 1 | 6 | 3 | 2 |
| 50 | p3c1, origin 1 | 6 | 2 | 2 |
| 51 | p3̅1m, origin 1 | 12 | 7 | 2 |
| 52 | p3̅1c, origin 1 | 12 | 5 | 2 |
Hexagonal (23)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 53 | p 6 | 6 | 2 | 1 |
| 54 | p6₁ | 6 | 1 | 1 |
| 55 | p6₂ | 6 | 2 | 1 |
| 56 | p6₃ | 6 | 2 | 1 |
| 57 | p6₄ | 6 | 2 | 1 |
| 58 | p6₅ | 6 | 1 | 1 |
| 59 | p6̅ | 6 | 6 | 1 |
| 60 | p 6/m | 12 | 6 | 1 |
| 61 | p6₃/m | 12 | 5 | 1 |
| 62 | p622 | 12 | 8 | 1 |
| 63 | p6₁22 | 12 | 3 | 1 |
| 64 | p6₂22 | 12 | 8 | 1 |
| 65 | p6₃22 | 12 | 6 | 1 |
| 66 | p6₄22 | 12 | 8 | 1 |
| 67 | p6₅22 | 12 | 3 | 1 |
| 68 | p6mm | 12 | 4 | 1 |
| 69 | p6cc | 12 | 2 | 1 |
| 70 | p6₃mc, origin 1 | 12 | 3 | 2 |
| 71 | p6̅m1, origin 1 | 12 | 9 | 2 |
| 72 | p6̅c2, origin 1 | 12 | 6 | 2 |
| 73 | p6/mmm | 24 | 12 | 1 |
| 74 | p6/mcc | 24 | 7 | 1 |
| 75 | p6₃/mmc, origin 1 | 24 | 8 | 2 |
Operations are counted per conventional cell (lattice centring included). Symbols follow the International Tables; the first listed setting is the standard one.