Origin at centre (-3)
| Asymmetric unit | 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 2/3; 0 ≤ z ≤ 1/2; x ≤ (1 + y)/2; y ≤ min(1 - x, (1 + x)/2) |
| Vertices | | 0, 0, 0 | 1/2, 0, 0 | 2/3, 1/3, 0 | 1/3, 2/3, 0 | 0, 1/2, 0 | | 0, 0, 1/2 | 1/2, 0, 1/2 | 2/3, 1/3, 1/2 | 1/3, 2/3, 1/2 | 0, 1/2, 1/2 |
|
| (1) 1 | (2) 3+ 0, 0, z | (3) 3- 0, 0, z |
| (4) -1 0, 0, 0 | (5) -3+ 0, 0, z; 0, 0, 0 | (6) -3- 0, 0, z; 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) -y, x - y, z | (3) -x + y, -x, z | | (4) -x, -y, -z | (5) y, -x + y, -z | (6) x - y, x, -z |
| no conditions |
| | | Special: as above, plus
|
| | 1/2, 0, 1/2 | 0, 1/2, 1/2 | 1/2, 1/2, 1/2 |
| no extra conditions |
| | 1/2, 0, 0 | 0, 1/2, 0 | 1/2, 1/2, 0 |
| no extra conditions |
| | no extra conditions |
| | no extra conditions |
| | no extra conditions |
| | no extra conditions |
Symmetry of special projections
Along [001] p6
a' = a b' = b
Origin at 0, 0, z | Along [100] p2
a' = 1/2(a + 2b) b' = c
Origin at x, 0, 0 | Along [210] p2
a' = 1/2b b' = c
Origin at x, 1/2x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P3 (143) | 1; 2; 3 |
| | | [3] P-1 (2) | 1; 4 |
| IIb | [3] R-3 (a' = a - b, b' = a + 2b, c' = 3c) (148); [3] R-3 (a' = 2a + b, b' = -a + b, c' = 3c) (148) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P-3 (c' = 2c) (147); [3] H-3 (a' = 3a, b' = 3b) (P-3, 147) |
Minimal non-isomorphic supergroups
| I | [2] P-31m (162); [2] P-31c (163); [2] P-3m1 (164); [2] P-3c1 (165); [2] P6/m (175); [2] P63/m (176) |
| II | [3] R-3 (obverse) (148); [3] R-3 (reverse) (148) |
