Crystal Lab › The 80 layer groups
The 80 layer groups
3D objects periodic in two directions. 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 (5)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 3 | p 1 1 2 | 2 | 5 | 1 |
| 4 | p 1 1 m | 2 | 2 | 1 |
| 5 | p 1 1 a | 2 | 1 | 3 |
| 6 | p 1 1 2/m | 4 | 10 | 1 |
| 7 | p 1 1 2/a | 4 | 5 | 3 |
Orthorhombic (41)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 8 | p 2 1 1 | 2 | 3 | 2 |
| 9 | p 21 1 1 | 2 | 1 | 2 |
| 10 | c 2 1 1 | 4 | 2 | 2 |
| 11 | p m 1 1 | 2 | 3 | 2 |
| 12 | p b 1 1 | 2 | 1 | 2 |
| 13 | c m 1 1 | 4 | 2 | 2 |
| 14 | p 2/m 1 1 | 4 | 9 | 2 |
| 15 | p 21/m 1 1 | 4 | 4 | 2 |
| 16 | p 2/b 1 1 | 4 | 4 | 2 |
| 17 | p 21/b 1 1 | 4 | 3 | 2 |
| 18 | c 2/m 1 1 | 8 | 6 | 2 |
| 19 | p 2 2 2 | 4 | 13 | 1 |
| 20 | p 21 2 2 | 4 | 4 | 2 |
| 21 | p 21 21 2 | 4 | 3 | 1 |
| 22 | c 2 2 2 | 8 | 8 | 1 |
| 23 | p m m 2 | 4 | 9 | 1 |
| 24 | p m a 2 | 4 | 4 | 2 |
| 25 | p b a 2 | 4 | 3 | 1 |
| 26 | c m m 2 | 8 | 6 | 1 |
| 27 | p m 2 m | 4 | 6 | 2 |
| 28 | p m 21 b | 4 | 3 | 2 |
| 29 | p b 21 m | 4 | 2 | 2 |
| 30 | p b 2 b | 4 | 3 | 2 |
| 31 | p m 2 a | 4 | 3 | 2 |
| 32 | p m 21 n | 4 | 2 | 2 |
| 33 | p b 21 a | 4 | 1 | 2 |
| 34 | p b 2 n | 4 | 2 | 2 |
| 35 | c m 2 m | 8 | 4 | 2 |
| 36 | c m 2 e | 8 | 3 | 2 |
| 37 | p m m m | 8 | 18 | 1 |
| 38 | p m a a | 8 | 11 | 2 |
| 39 | p b a n | 8 | 8 | 1 |
| 40 | p m a m | 8 | 8 | 2 |
| 41 | p m m a | 8 | 9 | 2 |
| 42 | p m a n | 8 | 6 | 2 |
| 43 | p b a a | 8 | 4 | 2 |
| 44 | p b a m | 8 | 6 | 1 |
| 45 | p b m a | 8 | 4 | 2 |
| 46 | p m m n | 8 | 6 | 1 |
| 47 | c m m m | 16 | 12 | 1 |
| 48 | c m m e | 16 | 10 | 1 |
Tetragonal (16)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 49 | p 4 | 4 | 4 | 1 |
| 50 | p -4 | 4 | 6 | 1 |
| 51 | p 4/m | 8 | 8 | 1 |
| 52 | p 4/n :2 | 8 | 5 | 2 |
| 53 | p 4 2 2 | 8 | 10 | 1 |
| 54 | p 4 21 2 | 8 | 5 | 1 |
| 55 | p 4 m m | 8 | 7 | 1 |
| 56 | p 4 b m | 8 | 4 | 1 |
| 57 | p -4 2 m | 8 | 10 | 1 |
| 58 | p -4 21 m | 8 | 5 | 1 |
| 59 | p -4 m 2 | 8 | 9 | 1 |
| 60 | p -4 b 2 | 8 | 6 | 1 |
| 61 | p 4/m m m | 16 | 14 | 1 |
| 62 | p 4/n b m :2 | 16 | 9 | 2 |
| 63 | p 4/m b m | 16 | 8 | 1 |
| 64 | p 4/n m m :2 | 16 | 8 | 2 |
Trigonal (8)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 65 | p 3 | 3 | 4 | 1 |
| 66 | p -3 | 6 | 5 | 1 |
| 67 | p 3 1 2 | 6 | 8 | 1 |
| 68 | p 3 2 1 | 6 | 5 | 1 |
| 69 | p 3 m 1 | 6 | 5 | 1 |
| 70 | p 3 1 m | 6 | 4 | 1 |
| 71 | p -3 1 m | 12 | 8 | 1 |
| 72 | p -3 m 1 | 12 | 7 | 1 |
Hexagonal (8)
| No. | Symbol | Operations | Wyckoff positions | Settings |
|---|---|---|---|---|
| 73 | p 6 | 6 | 4 | 1 |
| 74 | p -6 | 6 | 8 | 1 |
| 75 | p 6/m | 12 | 8 | 1 |
| 76 | p 6 2 2 | 12 | 9 | 1 |
| 77 | p 6 m m | 12 | 6 | 1 |
| 78 | p -6 m 2 | 12 | 10 | 1 |
| 79 | p -6 2 m | 12 | 8 | 1 |
| 80 | p 6/m m m | 24 | 12 | 1 |
Operations are counted per conventional cell (lattice centring included). Symbols follow the International Tables; the first listed setting is the standard one.