Origin at -1 on n, at 1/4, 1/4, 1/4 from -4
| Asymmetric unit | -1/4 ≤ x ≤ 1/4; -1/4 ≤ y ≤ 1/4; 0 ≤ z ≤ 1/2 |
| (1) 1 | (2) 2 1/4, 1/4, z | (3) 4+(0, 0, 1/2) -1/4, 1/4, z | (4) 4-(0, 0, 1/2) 1/4, -1/4, z |
| (5) -1 0, 0, 0 | (6) n(1/2, 1/2, 0) x, y, 0 | (7) -4+ 1/4, 1/4, z; 1/4, 1/4, 1/4 | (8) -4- 1/4, 1/4, z; 1/4, 1/4, 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 + 1/2, -y + 1/2, z | (3) -y, x + 1/2, z + 1/2 | (4) y + 1/2, -x, z + 1/2 | | (5) -x, -y, -z | (6) x + 1/2, y + 1/2, -z | (7) y, -x + 1/2, -z + 1/2 | (8) -y + 1/2, x, -z + 1/2 |
| hk0 : h + k = 2n
00l : l = 2n
h00 : h = 2n
|
| | | Special: as above, plus
|
| | 1/4, 1/4, z | 3/4, 3/4, z + 1/2 | 3/4, 3/4, -z | 1/4, 1/4, -z + 1/2 |
| hkl : h + k + l = 2n
|
| | 3/4, 1/4, z | 3/4, 1/4, z + 1/2 | 1/4, 3/4, -z | 1/4, 3/4, -z + 1/2 |
| hkl : l = 2n
|
| | 0, 0, 1/2 | 1/2, 1/2, 1/2 | 0, 1/2, 0 | 1/2, 0, 0 |
| hkl : h + k, h + l, k + l = 2n
|
| | 0, 0, 0 | 1/2, 1/2, 0 | 0, 1/2, 1/2 | 1/2, 0, 1/2 |
| hkl : h + k, h + l, k + l = 2n
|
| | 1/4, 1/4, 3/4 | 3/4, 3/4, 1/4 |
| hkl : h + k + l = 2n
|
| | 1/4, 1/4, 1/4 | 3/4, 3/4, 3/4 |
| hkl : h + k + l = 2n
|
Symmetry of special projections
Along [001] p4
a' = 1/2(a - b) b' = 1/2(a + b)
Origin at 1/4, 1/4, z | Along [100] p2mg
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/n (P2/c, 13) | 1; 2; 5; 6 |
| IIb | [2] F41/d (a' = 2a, b' = 2b, c' = 2c) (I41/a, 88) |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P42/n (c' = 3c) (86); [5] P42/n (a' = a + 2b, b' = -2a + b or a' = a - 2b, b' = 2a + b) (86) |
Minimal non-isomorphic supergroups
| I | [2] P42/nbc (133); [2] P42/nnm (134); [2] P42/nmc (137); [2] P42/ncm (138) |
| II | [2] C42/m (P42/m, 84); [2] I4/m (87); [2] P4/n (c' = 1/2c) (85) |
