Origin on 3 1 m
| Asymmetric unit | 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1; x ≤ (y + 1)/2; y ≤ min(1 - x, x) |
| Vertices | | 0, 0, 0 | 1/2, 0, 0 | 2/3, 1/3, 0 | 1/2, 1/2, 0 | | 0, 0, 1 | 1/2, 0, 1 | 2/3, 1/3, 1 | 1/2, 1/2, 1 |
|
| (1) 1 | (2) 3+ 0, 0, z | (3) 3- 0, 0, z |
| (4) m x, x, z | (5) m x, 0, z | (6) m 0, y, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -y, x - y, z | (3) -x + y, -x, z | | (4) y, x, z | (5) x - y, -y, z | (6) -x, -x + y, z |
| no conditions |
| | | Special: as above, plus
|
| | x, 0, z | 0, x, z | -x, -x, z |
| no extra conditions |
| | no extra conditions |
| | no extra conditions |
Symmetry of special projections
Along [001] p31m
a' = a b' = b
Origin at 0, 0, z | Along [100] p1m1
a' = 1/2(a + 2b) b' = c
Origin at x, 0, 0 | Along [210] p1
a' = 1/2b b' = c
Origin at x, 1/2x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P311 (P3, 143) | 1; 2; 3 |
| | ![[brace]](/graphics/sg/brace3.gif) | [3] P11m (Cm, 8) | 1; 4 | | | [3] P11m (Cm, 8) | 1; 5 | | | [3] P11m (Cm, 8) | 1; 6 |
|
| IIb | [2] P31c (c' = 2c) (159); [3] H31m (a' = 3a, b' = 3b) (P3m1, 156); [3] R3m (a' = a - b, b' = a + 2b, c' = 3c) (160); [3] R3m (a' = 2a + b, b' = -a + b, c' = 3c) (160) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P31m (c' = 2c) (157); [4] P31m (a' = 2a, b' = 2b) (157) |
Minimal non-isomorphic supergroups
| I | [2] P-31m (162); [2] P6mm (183); [2] P63cm (185); [2] P-62m (189) |
