| P212121 | D24 | 222 | Orthorhombic  |
| No. 19 | P212121 | Patterson symmetry Pmmm | |
Origin at midpoint of three non-intersecting pairs of parallel 21 axes
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Symmetry operations
| (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 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||
| General: | |||||||||
|
| h00 : h = 2n 0k0 : k = 2n 00l : l = 2n |
Symmetry of special projections
| Along [001] p2gg a' = a b' = b Origin at 1/4, 0, z | Along [100] p2gg a' = b b' = c Origin at x, 1/4, 0 | Along [010] p2gg a' = c b' = a Origin at 0, y, 1/4 |
Maximal non-isomorphic subgroups
| I | [2] P1121 (P21, 4) | 1; 2 | |
| [2] P1211 (P21, 4) | 1; 3 | ||
| [2] P2111 (P21, 4) | 1; 4 |
| IIa | none |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P212121 (a' = 3a or b' = 3b or c' = 3c) (19) |
Minimal non-isomorphic supergroups
| I | [2] Pbca (61); [2] Pnma (62); [2] P41212 (92); [2] P43212 (96); [3] P213 (198) |
| II | [2] A2122 (C2221, 20); [2] B2212 (C2221, 20); [2] C2221 (20); [2] I212121 (24); [2] P22121 (a' = 1/2a) (P21212, 18); [2] P21221 (b' = 1/2b) (P21212, 18); [2] P21212 (c' = 1/2c) (18) |
