Origin at centre (2/m) on 42
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
| (1) 1 | (2) 2 0, 0, z | (3) 4+(0, 0, 1/2) 0, 0, z | (4) 4-(0, 0, 1/2) 0, 0, z |
| (5) -1 0, 0, 0 | (6) m x, y, 0 | (7) -4+ 0, 0, z; 0, 0, 1/4 | (8) -4- 0, 0, z; 0, 0, 1/4 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -x, -y, z | (3) -y, x, z + 1/2 | (4) y, -x, z + 1/2 | | (5) -x, -y, -z | (6) x, y, -z | (7) y, -x, -z + 1/2 | (8) -y, x, -z + 1/2 |
| 00l : l = 2n
|
| | | Special: as above, plus
|
| | x, y, 0 | -x, -y, 0 | -y, x, 1/2 | y, -x, 1/2 |
| no extra conditions |
| | 0, 1/2, z | 1/2, 0, z + 1/2 | 0, 1/2, -z | 1/2, 0, -z + 1/2 |
| hkl : h + k + l = 2n
|
| | 1/2, 1/2, z | 1/2, 1/2, z + 1/2 | 1/2, 1/2, -z | 1/2, 1/2, -z + 1/2 |
| hkl : l = 2n
|
| | 0, 0, z | 0, 0, z + 1/2 | 0, 0, -z | 0, 0, -z + 1/2 |
| hkl : l = 2n
|
| | 1/2, 1/2, 1/4 | 1/2, 1/2, 3/4 |
| hkl : l = 2n
|
| | hkl : l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | 1/2, 1/2, 0 | 1/2, 1/2, 1/2 |
| hkl : l = 2n
|
| | hkl : l = 2n
|
Symmetry of special projections
Along [001] p4
a' = a b' = b
Origin at 0, 0, z | Along [100] p2mm
a' = b b' = c
Origin at x, 0, 0 | Along [110] p2mm
a' = 1/2(-a + b) b' = c
Origin at x, x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P-4 (81) | 1; 2; 7; 8 |
| | | [2] P42 (77) | 1; 2; 3; 4 |
| | | [2] P2/m (10) | 1; 2; 5; 6 |
| IIb | [2] C42/e (a' = 2a, b' = 2b) (P42/n, 86) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] C42/m (a' = 2a, b' = 2b) (P42/m, 84); [3] P42/m (c' = 3c) (84) |
Minimal non-isomorphic supergroups
| I | [2] P42/mmc (131); [2] P42/mcm (132); [2] P42/mbc (135); [2] P42/mnm (136) |
| II | [2] I4/m (87); [2] P4/m (c' = 1/2c) (83) |
