Origin on 3
| Asymmetric unit | 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 2/3; 0 ≤ z ≤ 1; 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 | 1/2, 0, 1 | 2/3, 1/3, 1 | 1/3, 2/3, 1 | 0, 1/2, 1 |
|
| (1) 1 | (2) 3+ 0, 0, z | (3) 3- 0, 0, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -y, x - y, z | (3) -x + y, -x, z |
| no conditions |
| | | Special: as above, plus
|
| | no extra conditions |
| | no extra conditions |
| | no extra conditions |
Symmetry of special projections
Along [001] p3
a' = a b' = b
Origin at 0, 0, z | Along [100] p1
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
| IIb | [3] P32 (c' = 3c) (145); [3] P31 (c' = 3c) (144); [3] R3 (a' = a - b, b' = a + 2b, c' = 3c) (146); [3] R3 (a' = 2a + b, b' = -a + b, c' = 3c) (146) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P3 (c' = 2c) (143); [3] H3 (a' = 3a, b' = 3b) (P3, 143) |
Minimal non-isomorphic supergroups
| I | [2] P-3 (147); [2] P312 (149); [2] P321 (150); [2] P3m1 (156); [2] P31m (157); [2] P3c1 (158); [2] P31c (159); [2] P6 (168); [2] P63 (173); [2] P-6 (174) |
| II | [3] R3 (obverse) (146); [3] R3 (reverse) (146) |
