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
Triclinic (2)
Monoclinic (10)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 3 | pc 2 1 1 | 2 | 3 | 6 |
| 4 | pc m 1 1 | 2 | 2 | 6 |
| 5 | pc c 1 1 | 2 | 1 | 6 |
| 6 | pc 2/m 1 1 | 4 | 6 | 6 |
| 7 | pc 2/c 1 1 | 4 | 3 | 6 |
| 8 | pc 1 1 2 | 2 | 2 | 6 |
| 9 | pc 1 1 21 | 2 | 1 | 6 |
| 10 | pc 1 1 m | 2 | 3 | 6 |
| 11 | pc 1 1 2/m | 4 | 6 | 6 |
| 12 | pc 1 1 21/m | 4 | 3 | 6 |
Orthorhombic (10)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 13 | pc 2 2 2 | 4 | 8 | 6 |
| 14 | pc 2 2 21 | 4 | 3 | 6 |
| 15 | pc m m 2 | 4 | 4 | 6 |
| 16 | pc c c 2 | 4 | 2 | 6 |
| 17 | pc m c 21 | 4 | 2 | 6 |
| 18 | pc 2 m m | 4 | 6 | 6 |
| 19 | pc 2 c m | 4 | 3 | 6 |
| 20 | pc m m m | 8 | 12 | 6 |
| 21 | pc c c m | 8 | 7 | 6 |
| 22 | pc m c m | 8 | 6 | 6 |
Tetragonal (19)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 23 | p 4 | 4 | 2 | 1 |
| 24 | p 41 | 4 | 1 | 1 |
| 25 | p 42 | 4 | 2 | 1 |
| 26 | p 43 | 4 | 1 | 1 |
| 27 | p -4 | 4 | 4 | 1 |
| 28 | p 4/m | 8 | 6 | 1 |
| 29 | p 42/m | 8 | 5 | 1 |
| 30 | p 4 2 2 | 8 | 8 | 1 |
| 31 | p 41 2 2 | 8 | 3 | 1 |
| 32 | p 42 2 2 | 8 | 8 | 1 |
| 33 | p 43 2 2 | 8 | 3 | 1 |
| 34 | p 4 m m | 8 | 4 | 1 |
| 35 | p 42 c m :1 | 8 | 3 | 2 |
| 36 | p 4 c c | 8 | 2 | 1 |
| 37 | p -4 2 m :1 | 8 | 7 | 2 |
| 38 | p -4 2 c :1 | 8 | 6 | 2 |
| 39 | p 4/m m m | 16 | 12 | 1 |
| 40 | p 4/m c c | 16 | 7 | 1 |
| 41 | p 42/m m c :1 | 16 | 9 | 2 |
Trigonal (11)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 42 | p 3 | 3 | 2 | 1 |
| 43 | p 31 | 3 | 1 | 1 |
| 44 | p 32 | 3 | 1 | 1 |
| 45 | p -3 | 6 | 4 | 1 |
| 46 | p 3 1 2 :1 | 6 | 6 | 2 |
| 47 | p 31 1 2 :1 | 6 | 3 | 2 |
| 48 | p 32 1 2 :1 | 6 | 3 | 2 |
| 49 | p 3 m 1 :1 | 6 | 3 | 2 |
| 50 | p 3 c 1 :1 | 6 | 2 | 2 |
| 51 | p -3 1 m :1 | 12 | 7 | 2 |
| 52 | p -3 1 c :1 | 12 | 5 | 2 |
Hexagonal (23)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 53 | p 6 | 6 | 2 | 1 |
| 54 | p 61 | 6 | 1 | 1 |
| 55 | p 62 | 6 | 2 | 1 |
| 56 | p 63 | 6 | 2 | 1 |
| 57 | p 64 | 6 | 2 | 1 |
| 58 | p 65 | 6 | 1 | 1 |
| 59 | p -6 | 6 | 6 | 1 |
| 60 | p 6/m | 12 | 6 | 1 |
| 61 | p 63/m | 12 | 5 | 1 |
| 62 | p 6 2 2 | 12 | 8 | 1 |
| 63 | p 61 2 2 | 12 | 3 | 1 |
| 64 | p 62 2 2 | 12 | 8 | 1 |
| 65 | p 63 2 2 | 12 | 6 | 1 |
| 66 | p 64 2 2 | 12 | 8 | 1 |
| 67 | p 65 2 2 | 12 | 3 | 1 |
| 68 | p 6 m m | 12 | 4 | 1 |
| 69 | p 6 c c | 12 | 2 | 1 |
| 70 | p 63 m c :1 | 12 | 3 | 2 |
| 71 | p -6 m 1 :1 | 12 | 9 | 2 |
| 72 | p -6 c 2 :1 | 12 | 6 | 2 |
| 73 | p 6/m m m | 24 | 12 | 1 |
| 74 | p 6/m c c | 24 | 7 | 1 |
| 75 | p 63/m m c :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.