Origin on 3 c 1
| 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) c x, -x, z | (5) c x, 2x, z | (6) c 2x, x, z |
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) -y, -x, z + 1/2 | (5) -x + y, y, z + 1/2 | (6) x, x - y, z + 1/2 |
| h-h0l : l = 2n
000l : l = 2n
|
| | | Special: as above, plus
|
| | 2/3, 1/3, z | 2/3, 1/3, z + 1/2 |
| hkil : l = 2n
|
| | 1/3, 2/3, z | 1/3, 2/3, z + 1/2 |
| hkil : l = 2n
|
| | hkil : l = 2n
|
Symmetry of special projections
Along [001] p3m1
a' = a b' = b
Origin at 0, 0, z | Along [100] p1
a' = 1/2(a + 2b) b' = 1/2c
Origin at x, 0, 0 | Along [210] p1g1
a' = 1/2b b' = c
Origin at x, 1/2x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P311 (P3, 143) | 1; 2; 3 |
| | ![[brace]](/graphics/sg/brace3.gif) | [3] P1c1 (Cc, 9) | 1; 4 | | | [3] P1c1 (Cc, 9) | 1; 5 | | | [3] P1c1 (Cc, 9) | 1; 6 |
|
| IIb | [3] H3c1 (a' = 3a, b' = 3b) (P31c, 159) |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P3c1 (c' = 3c) (158); [4] P3c1 (a' = 2a, b' = 2b) (158) |
Minimal non-isomorphic supergroups
| I | [2] P-3c1 (165); [2] P6cc (184); [2] P63cm (185); [2] P-6c2 (188) |
| II | [3] H3c1 (P31c, 159); [3] R3c (obverse) (161); [3] R3c (reverse) (161); [2] P3m1 (c' = 1/2c) (156) |
