Origin at 3 2
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/2; z ≤ min(x, y, 1 - x, 1 - y) |
| Vertices | | 0, 0, 0 | 1, 0, 0 | 1, 1, 0 | 0, 1, 0 | 1/2, 1/2, 1/2 |
|
| (1) 1 | (2) 3+ x, x, x | (3) 3- x, x, x |
| (4) 2 -x, 0, x | (5) 2 x, -x, 0 | (6) 2 0, y, -y |
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) z, x, y | (3) y, z, x | | (4) -z, -y, -x | (5) -y, -x, -z | (6) -x, -z, -y |
| no conditions |
| | | Special: as above, plus
|
| | 1/2, y, -y | -y, 1/2, y | y, -y, 1/2 |
| no extra conditions |
| | 0, y, -y | -y, 0, y | y, -y, 0 |
| no extra conditions |
| | no extra conditions |
| | no extra conditions |
| | no extra conditions |
Symmetry of special projections
Along [111] p3m1
a' = 1/3(2a - b - c) b' = 1/3(-a + 2b - c)
Origin at x, x, x | Along [1-10] p2
a' = 1/2(a + b - 2c) b' = c
Origin at x, -x, 0 | Along [2-1-1] p11m
a' = 1/2(b - c) b' = 1/3(a + b + c)
Origin at 2x, -x, -x |
Maximal non-isomorphic subgroups
| I | | [2] R31 (R3, 146) | 1; 2; 3 |
| | ![[brace]](/graphics/sg/brace3.gif) | [3] R12 (C2, 5) | 1; 4 | | | [3] R12 (C2, 5) | 1; 5 | | | [3] R12 (C2, 5) | 1; 6 |
|
| IIb | [3] P321 (a' = a - b, b' = b - c, c' = a + b + c) (150); [3] P3121 (a' = a - b, b' = b - c, c' = a + b + c) (152); [3] P3221 (a' = a - b, b' = b - c, c' = a + b + c) (154) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] R32 (a' = b + c, b' = a + c, c' = a + b) (155); [4] R32 (a' = -a + b + c, b' = a - b + c, c' = a + b - c) (155) |
Minimal non-isomorphic supergroups
| I | [2] R-3m (166); [2] R-3c (167); [4] P432 (207); [4] P4232 (208); [4] F432 (209); [4] F4132 (210); [4] I432 (211); [4] P4332 (212); [4] P4132 (213); [4] I4132 (214) |
| II | [3] P312 (a' = 1/3(2a - b - c), b' = 1/3(-a + 2b - c), c' = 1/3(a + b + c)) (149) |
