| Fmm2 | C2v18 | mm2 | Orthorhombic  |
| No. 42 | Fmm2 | Patterson symmetry Fmmm | |
Origin on m m 2
| Asymmetric unit | 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2 0, 0, z | (3) m x, 0, z | (4) m 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, 1/4, z | (4) n(0, 1/2, 1/2) 0, y, z |
For (1/2, 0, 1/2)+ set
| (1) t(1/2, 0, 1/2) | (2) 2(0, 0, 1/2) 1/4, 0, z | (3) n(1/2, 0, 1/2) x, 0, z | (4) c 1/4, y, z |
For (1/2, 1/2, 0)+ set
| (1) t(1/2, 1/2, 0) | (2) 2 1/4, 1/4, z | (3) a x, 1/4, z | (4) b 1/4, y, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); t(1/2, 0, 1/2); (2); (3)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||
| (0, 0, 0)+ (0, 1/2, 1/2)+ (1/2, 0, 1/2)+ (1/2, 1/2, 0)+ | General: | ||||||||
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| hkl : h + k, h + l, 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 | |||||||
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| no extra conditions | |||||
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| no extra conditions | |||||
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| hkl : h = 2n | |||||
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| no extra conditions |
Symmetry of special projections
| Along [001] p2mm a' = 1/2a 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' = 1/2a Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | [2] F1m1 (Cm, 8) | (1; 3)+ | |
| [2] Fm11 (Cm, 8) | (1; 4)+ | ||
| [2] F112 (C2, 5) | (1; 2)+ |
| IIa | [2] Aea2 (41) | 1; 2; (1; 2) + (0, 1/2, 1/2); (3; 4) + (1/2, 0, 1/2); (3; 4) + (1/2, 1/2, 0) | |
| [2] Bbe2 (Aea2, 41) | 1; 2; (1; 2) + (1/2, 0, 1/2); (3; 4) + (0, 1/2, 1/2); (3; 4) + (1/2, 1/2, 0) | ||
| [2] Ama2 (40) | 1; 4; (1; 4) + (0, 1/2, 1/2); (2; 3) + (1/2, 0, 1/2); (2; 3) + (1/2, 1/2, 0) | ||
| [2] Bbm2 (Ama2, 40) | 1; 3; (1; 3) + (1/2, 0, 1/2); (2; 4) + (0, 1/2, 1/2); (2; 4) + (1/2, 1/2, 0) | ||
| [2] Bme2 (Aem2, 39) | 1; 4; (1; 4) + (1/2, 0, 1/2); (2; 3) + (0, 1/2, 1/2); (2; 3) + (1/2, 1/2, 0) | ||
| [2] Aem2 (39) | 1; 3; (1; 3) + (0, 1/2, 1/2); (2; 4) + (1/2, 0, 1/2); (2; 4) + (1/2, 1/2, 0) | ||
| [2] Amm2 (38) | 1; 2; 3; 4; (1; 2; 3; 4) + (0, 1/2, 1/2) | ||
| [2] Bmm2 (Amm2, 38) | 1; 2; 3; 4; (1; 2; 3; 4) + (1/2, 0, 1/2) | ||
| [2] Ccc2 (37) | 1; 2; (1; 2) + (1/2, 1/2, 0); (3; 4) + (0, 1/2, 1/2); (3; 4) + (1/2, 0, 1/2) | ||
| [2] Ccm21 (Cmc21, 36) | 1; 3; (1; 3) + (1/2, 1/2, 0); (2; 4) + (0, 1/2, 1/2); (2; 4) + (1/2, 0, 1/2) | ||
| [2] Cmc21 (36) | 1; 4; (1; 4) + (1/2, 1/2, 0); (2; 3) + (0, 1/2, 1/2); (2; 3) + (1/2, 0, 1/2) | ||
| [2] Cmm2 (35) | 1; 2; 3; 4; (1; 2; 3; 4) + (1/2, 1/2, 0) |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] Fmm2 (a' = 3a or b' = 3b) (42); [3] Fmm2 (c' = 3c) (42) |
Minimal non-isomorphic supergroups
| I | [2] Fmmm (69); [2] I4mm (107); [2] I4cm (108); [2] I-42m (121) |
| II | [2] Pmm2 (a' = 1/2a, b' = 1/2b, c' = 1/2c) (25) |
