Origin at -4
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4 |
| (1) 1 | (2) 2 0, 0, z | (3) -4+ 0, 0, z; 0, 0, 0 | (4) -4- 0, 0, z; 0, 0, 0 |
| (5) n(1/2, 0, 1/2) x, 1/4, z | (6) n(0, 1/2, 1/2) 1/4, y, z | (7) 2(1/2, 1/2, 0) x, x, 1/4 | (8) 2 x, -x + 1/2, 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 | (4) -y, x, -z | | (5) x + 1/2, -y + 1/2, z + 1/2 | (6) -x + 1/2, y + 1/2, z + 1/2 | (7) y + 1/2, x + 1/2, -z + 1/2 | (8) -y + 1/2, -x + 1/2, -z + 1/2 |
| 0kl : k + l = 2n
00l : l = 2n
h00 : h = 2n
|
| | | Special: as above, plus
|
| | 0, 1/2, z | 1/2, 0, -z | 1/2, 0, z + 1/2 | 0, 1/2, -z + 1/2 |
| hkl : h + k + l = 2n
|
| | x, x + 1/2, 1/4 | -x, -x + 1/2, 1/4 | x + 1/2, -x, 3/4 | -x + 1/2, x, 3/4 |
| no extra conditions |
| | x, -x + 1/2, 1/4 | -x, x + 1/2, 1/4 | -x + 1/2, -x, 3/4 | x + 1/2, x, 3/4 |
| no extra conditions |
| | 0, 0, z | 0, 0, -z | 1/2, 1/2, z + 1/2 | 1/2, 1/2, -z + 1/2 |
| hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
Symmetry of special projections
Along [001] p4gm
a' = a b' = b
Origin at 0, 0, z | Along [100] c1m1
a' = b b' = c
Origin at x, 0, 0 | Along [110] p2mm
a' = 1/2(-a + b) b' = c
Origin at x, x, 1/4 |
Maximal non-isomorphic subgroups
| I | | [2] P-411 (P-4, 81) | 1; 2; 3; 4 |
| | | [2] P2n1 (Pnn2, 34) | 1; 2; 5; 6 |
| | | [2] P212 (C222, 21) | 1; 2; 7; 8 |
| IIb | [2] F-4d2 (a' = 2a, b' = 2b, c' = 2c) (I-42d, 122) |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P-4n2 (c' = 3c) (118); [9] P-4n2 (a' = 3a, b' = 3b) (118) |
Minimal non-isomorphic supergroups
| I | [2] P4/nnc (126); [2] P4/mnc (128); [2] P42/nnm (134); [2] P42/mnm (136) |
| II | [2] C-4c2 (P-42c, 112); [2] I-4m2 (119); [2] P-4b2 (c' = 1/2c) (117) |
