Origin at centre (-3)
| 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) -1 0, 0, 0 | (5) -3+ x, x, x; 0, 0, 0 | (6) -3- x, x, x; 0, 0, 0 |
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) -x, -y, -z | (5) -z, -x, -y | (6) -y, -z, -x |
| no conditions |
| | | Special: as above, plus
|
| | 0, 1/2, 1/2 | 1/2, 0, 1/2 | 1/2, 1/2, 0 |
| no extra conditions |
| | 1/2, 0, 0 | 0, 1/2, 0 | 0, 0, 1/2 |
| no extra conditions |
| | no extra conditions |
| | no extra conditions |
| | no extra conditions |
Symmetry of special projections
Along [111] p6
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] p2
a' = 1/2(b - c) b' = 1/3(a + b + c)
Origin at 2x, -x, -x |
Maximal non-isomorphic subgroups
| I | | [2] R3 (146) | 1; 2; 3 |
| | | [3] R-1 (P-1, 2) | 1; 4 |
| IIb | [3] P-3 (a' = a - b, b' = b - c, c' = a + b + c) (147) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] R-3 (a' = b + c, b' = a + c, c' = a + b) (148); [4] R-3 (a' = -a + b + c, b' = a - b + c, c' = a + b - c) (148) |
Minimal non-isomorphic supergroups
| I | [2] R-3m (166); [2] R-3c (167); [4] Pm-3 (200); [4] Pn-3 (201); [4] Fm-3 (202); [4] Fd-3 (203); [4] Im-3 (204); [4] Pa-3 (205); [4] Ia-3 (206) |
| II | [3] P-3 (a' = 1/3(2a - b - c), b' = 1/3(-a + 2b - c), c' = 1/3(a + b + c)) (147) |
