| I212121 | D29 | 222 | Orthorhombic  |
| No. 24 | I212121 | Patterson symmetry Immm | |
Origin at midpoint of three non-intersecting pairs of parallel 2 axes
| 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) 1/4, 0, z | (3) 2(0, 1/2, 0) 0, y, 1/4 | (4) 2(1/2, 0, 0) x, 1/4, 0 |
For (1/2, 1/2, 1/2)+ set
| (1) t(1/2, 1/2, 1/2) | (2) 2 0, 1/4, z | (3) 2 1/4, y, 0 | (4) 2 x, 0, 1/4 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||
| (0, 0, 0)+ (1/2, 1/2, 1/2)+ | General: | ||||||||
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| hkl : h + k + l = 2n 0kl : k + l = 2n h0l : h + l = 2n hk0 : h + k = 2n h00 : h = 2n 0k0 : k = 2n 00l : l = 2n |
| Special: as above, plus | |||||||
|
| hk0 : h = 2n | |||||
|
| h0l : h = 2n | |||||
|
| 0kl : k = 2n |
Symmetry of special projections
| Along [001] c2mm a' = a b' = b Origin at 1/4, 0, z | Along [100] c2mm a' = b b' = c Origin at x, 1/4, 0 | Along [010] c2mm a' = c b' = a Origin at 0, y, 1/4 |
Maximal non-isomorphic subgroups
| I | [2] I1121 (C2, 5) | (1; 2)+ | |
| [2] I1211 (C2, 5) | (1; 3)+ | ||
| [2] I2111 (C2, 5) | (1; 4)+ |
| IIa | [2] P212121 (19) | 1; 2; 3; 4 | |
| [2] P2221 (17) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | ||
| [2] P2212 (P2221, 17) | 1; 3; (2; 4) + (1/2, 1/2, 1/2) | ||
| [2] P2122 (P2221, 17) | 1; 4; (2; 3) + (1/2, 1/2, 1/2) |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] I212121 (a' = 3a or b' = 3b or c' = 3c) (24) |
Minimal non-isomorphic supergroups
| I | [2] Ibca (73); [2] Imma (74); [2] I4122 (98); [2] I-42d (122); [3] I213 (199) |
| II | [2] A222 (a' = 1/2a) (C222, 21); [2] B222 (b' = 1/2b) (C222, 21); [2] C222 (c' = 1/2c) (21) |
