Origin on 2[1 1 0] at 31 (1, 1, 2) 1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/6 |
| Vertices | | 0, 0, 0 | 1, 0, 0 | 1, 1, 0 | 0, 1, 0 | | 0, 0, 1/6 | 1, 0, 1/6 | 1, 1, 1/6 | 0, 1, 1/6 |
|
| (1) 1 | (2) 3+(0, 0, 1/3) 0, 0, z | (3) 3-(0, 0, 2/3) 0, 0, z |
| (4) 2 x, x, 0 | (5) 2 x, 0, 1/3 | (6) 2 0, y, 1/6 |
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 + 1/3 | (3) -x + y, -x, z + 2/3 | | (4) y, x, -z | (5) x - y, -y, -z + 2/3 | (6) -x, -x + y, -z + 1/3 |
| 000l : l = 3n
|
| | | Special: as above, plus
|
| | x, 0, 5/6 | 0, x, 1/6 | -x, -x, 1/2 |
| no extra conditions |
| | x, 0, 1/3 | 0, x, 2/3 | -x, -x, 0 |
| no extra conditions |
Symmetry of special projections
Along [001] p31m
a' = a b' = b
Origin at 0, 0, z | Along [100] p2
a' = 1/2(a + 2b) b' = c
Origin at x, 0, 1/3 | Along [210] p11m
a' = 1/2b b' = c
Origin at x, 1/2x, 1/6 |
Maximal non-isomorphic subgroups
| I | | [2] P3111 (P31, 144) | 1; 2; 3 |
| | ![[brace]](/graphics/sg/brace3.gif) | [3] P121 (C2, 5) | 1; 4 | | | [3] P121 (C2, 5) | 1; 5 | | | [3] P121 (C2, 5) | 1; 6 |
|
| IIb | [3] H3121 (a' = 3a, b' = 3b) (P3112, 151) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P3221 (c' = 2c) (154); [4] P3121 (a' = 2a, b' = 2b) (152); [7] P3121 (c' = 7c) (152) |
Minimal non-isomorphic supergroups
| I | [2] P6122 (178); [2] P6422 (181) |
| II | [3] H3121 (P3112, 151); [3] R32 (obverse) (155); [3] R32 (reverse) (155); [3] P321 (c' = 1/3c) (150) |
