| P21212 | D23 | 222 | Orthorhombic  |
| No. 18 | P21212 | Patterson symmetry Pmmm | |
Origin at intersection of 2 with perpendicular plane containing 21 axes
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Symmetry operations
| (1) 1 | (2) 2 0, 0, z | (3) 2(0, 1/2, 0) 1/4, y, 0 | (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 |
| Special: as above, plus | |||||||
|
| hk0 : h + k = 2n | |||||
|
| hk0 : h + k = 2n |
Symmetry of special projections
| Along [001] p2gg a' = a b' = b Origin at 0, 0, z | Along [100] p2mg a' = b b' = c Origin at x, 1/4, 0 | Along [010] p2gm a' = c b' = a Origin at 1/4, y, 0 |
Maximal non-isomorphic subgroups
| I | [2] P1211 (P21, 4) | 1; 3 | |
| [2] P2111 (P21, 4) | 1; 4 | ||
| [2] P112 (P2, 3) | 1; 2 |
| IIa | none |
| IIb | [2] P212121 (c' = 2c) (19) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P21212 (c' = 2c) (18); [3] P21212 (a' = 3a or b' = 3b) (18) |
Minimal non-isomorphic supergroups
| I | [2] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pmmn (59); [2] Pbcn (60); [2] P4212 (90); [2] P42212 (94); [2] P-421m (113); [2] P-421c (114) |
| II | [2] A2122 (C2221, 20); [2] B2212 (C2221, 20); [2] C222 (21); [2] I222 (23); [2] P2212 (a' = 1/2a) (P2221, 17); [2] P2122 (b' = 1/2b) (P2221, 17) |
