Origin on 3 m 1 on 63 m c
| Asymmetric unit | 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 1/3; 0 ≤ z ≤ 1; x ≤ (1 + y)/2; y ≤ x/2 |
| Vertices | | 0, 0, 0 | 1/2, 0, 0 | 2/3, 1/3, 0 | | 0, 0, 1 | 1/2, 0, 1 | 2/3, 1/3, 1 |
|
| (1) 1 | (2) 3+ 0, 0, z | (3) 3- 0, 0, z |
| (4) 2(0, 0, 1/2) 0, 0, z | (5) 6-(0, 0, 1/2) 0, 0, z | (6) 6+(0, 0, 1/2) 0, 0, z |
| (7) m x, -x, z | (8) m x, 2x, z | (9) m 2x, x, z |
| (10) c x, x, z | (11) c x, 0, z | (12) c 0, y, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4); (7)
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 + 1/2 | (5) y, -x + y, z + 1/2 | (6) x - y, x, z + 1/2 | | (7) -y, -x, z | (8) -x + y, y, z | (9) x, x - y, z | | (10) y, x, z + 1/2 | (11) x - y, -y, z + 1/2 | (12) -x, -x + y, z + 1/2 |
| hh(-2h)l : l = 2n
000l : l = 2n
|
| | | Special: as above, plus
|
| | x, -x, z | x, 2x, z | (-2x), -x, z | -x, x, z + 1/2 | -x, (-2x), z + 1/2 | 2x, x, z + 1/2 |
| no extra conditions |
| | 1/3, 2/3, z | 2/3, 1/3, z + 1/2 |
| hkil : l = 2n
or h - k = 3n + 1
or h - k = 3n + 2
|
| | hkil : l = 2n
|
Symmetry of special projections
Along [001] p6mm
a' = a b' = b
Origin at 0, 0, z | Along [100] p1g1
a' = 1/2(a + 2b) b' = c
Origin at x, 0, 0 | Along [210] p1m1
a' = 1/2b b' = 1/2c
Origin at x, 1/2x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P6311 (P63, 173) | 1; 2; 3; 4; 5; 6 |
| | | [2] P31c (159) | 1; 2; 3; 10; 11; 12 |
| | | [2] P3m1 (156) | 1; 2; 3; 7; 8; 9 |
| | ![[brace]](/graphics/sg/brace3.gif) | [3] P21mc (Cmc21, 36) | 1; 4; 7; 10 | | | [3] P21mc (Cmc21, 36) | 1; 4; 8; 11 | | | [3] P21mc (Cmc21, 36) | 1; 4; 9; 12 |
|
| IIb | [3] H63mc (a' = 3a, b' = 3b) (P63cm, 185) |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P63mc (c' = 3c) (186); [4] P63mc (a' = 2a, b' = 2b) (186) |
Minimal non-isomorphic supergroups
| II | [3] H63mc (P63cm, 185); [2] P6mm (c' = 1/2c) (183) |
