| Aem2 | C2v15 | mm2 | Orthorhombic  |
| No. 39 | Aem2 | Patterson symmetry Ammm (Cmmm) | |
Origin on e c 2
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2 0, 0, z | (3) m x, 1/4, z | (4) b 0, y, z |
For (0, 1/2, 1/2)+ set
| (1) t(0, 1/2, 1/2) | (2) 2(0, 0, 1/2) 0, 1/4, z | (3) c x, 0, z | (4) c 0, y, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2); (3)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||
| (0, 0, 0)+ (0, 1/2, 1/2)+ | General: | ||||||||
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| hkl : k + l = 2n 0kl : k, l = 2n h0l : l = 2n hk0 : k = 2n 0k0 : k = 2n 00l : l = 2n |
| Special: as above, plus | |||||||
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| no extra conditions | |||||
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| hkl : k = 2n | |||||
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| hkl : k = 2n |
Symmetry of special projections
| Along [001] p2mm a' = a b' = 1/2b Origin at 0, 0, z | Along [100] p1m1 a' = 1/2b b' = 1/2c Origin at x, 0, 0 | Along [010] p11m a' = 1/2c b' = a Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | [2] A1m1 (Cm, 8) | (1; 3)+ | |
| [2] Ae11 (Pc, 7) | (1; 4)+ | ||
| [2] A112 (C2, 5) | (1; 2)+ |
| IIa | [2] Pbc21 (Pca21, 29) | 1; 4; (2; 3) + (0, 1/2, 1/2) | |
| [2] Pbm2 (Pma2, 28) | 1; 2; 3; 4 | ||
| [2] Pcc2 (27) | 1; 2; (3; 4) + (0, 1/2, 1/2) | ||
| [2] Pcm21 (Pmc21, 26) | 1; 3; (2; 4) + (0, 1/2, 1/2) |
| IIb | [2] Ibm2 (a' = 2a) (Ima2, 46); [2] Iba2 (a' = 2a) (45); [2] Aea2 (a' = 2a) (41) |
Maximal isomorphic subgroups of lowest index
| IIc | [2] Aem2 (a' = 2a) (39); [3] Aem2 (b' = 3b) (39); [3] Aem2 (c' = 3c) (39) |
Minimal non-isomorphic supergroups
| I | [2] Cmce (64); [2] Cmme (67) |
| II | [2] Fmm2 (42); [2] Pmm2 (b' = 1/2b, c' = 1/2c) (25) |
