| C2221 | D25 | 222 | Orthorhombic  |
| No. 20 | C2221 | Patterson symmetry Cmmm | |
Origin at 2 1 21
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2(0, 0, 1/2) 0, 0, z | (3) 2 0, y, 1/4 | (4) 2 x, 0, 0 |
For (1/2, 1/2, 0)+ set
| (1) t(1/2, 1/2, 0) | (2) 2(0, 0, 1/2) 1/4, 1/4, z | (3) 2(0, 1/2, 0) 1/4, y, 1/4 | (4) 2(1/2, 0, 0) x, 1/4, 0 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||
| (0, 0, 0)+ (1/2, 1/2, 0)+ | General: | ||||||||
|
| hkl : h + k = 2n 0kl : k = 2n h0l : h = 2n hk0 : h + k = 2n h00 : h = 2n 0k0 : k = 2n 00l : l = 2n |
| Special: as above, plus | |||||||
|
| h0l : l = 2n | |||||
|
| 0kl : l = 2n |
Symmetry of special projections
| Along [001] c2mm a' = a b' = b Origin at 0, 0, z | Along [100] p2gm a' = 1/2b b' = c Origin at x, 0, 0 | Along [010] p2mg a' = c b' = 1/2a Origin at 0, y, 1/4 |
Maximal non-isomorphic subgroups
| I | [2] C121 (C2, 5) | (1; 3)+ | |
| [2] C211 (C2, 5) | (1; 4)+ | ||
| [2] C1121 (P21, 4) | (1; 2)+ |
| IIa | [2] P212121 (19) | 1; 2; (3; 4) + (1/2, 1/2, 0) | |
| [2] P21221 (P21212, 18) | 1; 3; (2; 4) + (1/2, 1/2, 0) | ||
| [2] P22121 (P21212, 18) | 1; 4; (2; 3) + (1/2, 1/2, 0) | ||
| [2] P2221 (17) | 1; 2; 3; 4 |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] C2221 (a' = 3a or b' = 3b) (20); [3] C2221 (c' = 3c) (20) |
Minimal non-isomorphic supergroups
| I | [2] Cmcm (63); [2] Cmce (64); [2] P4122 (91); [2] P41212 (92); [2] P4322 (95); [2] P43212 (96); [3] P6122 (178); [3] P6522 (179); [3] P6322 (182) |
| II | [2] F222 (22); [2] P2221 (a' = 1/2a, b' = 1/2b) (17); [2] C222 (c' = 1/2c) (21) |
