| I-42d | D2d12 | -42m | Tetragonal  |
| No. 122 | I-42d | Patterson symmetry I4/mmm | |
Origin at -4
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/8 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2 0, 0, z | (3) -4+ 0, 0, z; 0, 0, 0 | (4) -4- 0, 0, z; 0, 0, 0 |
| (5) 2 1/4, y, 3/8 | (6) 2(1/2, 0, 0) x, 0, 3/8 | (7) d(1/4, -1/4, 3/4) x + 1/4, -x, z | (8) d(1/4, 1/4, 3/4) x + 1/4, x, z |
For (1/2, 1/2, 1/2)+ set
| (1) t(1/2, 1/2, 1/2) | (2) 2(0, 0, 1/2) 1/4, 1/4, z | (3) -4+ 1/2, 0, z; 1/2, 0, 1/4 | (4) -4- 0, 1/2, z; 0, 1/2, 1/4 |
| (5) 2(0, 1/2, 0) 0, y, 1/8 | (6) 2 x, 1/4, 1/8 | (7) d(-1/4, 1/4, 1/4) x + 1/4, -x, z | (8) d(1/4, 1/4, 1/4) x - 1/4, x, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3); (5)
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 hk0 : h + k = 2n 0kl : k + l = 2n hhl : 2h + l = 4n 00l : l = 4n h00 : h = 2n h-h0 : h = 2n |
| Special: as above, plus | |||||||||
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| no extra conditions | |||||||
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| hkl : l = 2n + 1 or 2h + l = 4n | |||||||
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| hkl : l = 2n + 1 or 2h + l = 4n | |||||||
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| hkl : l = 2n + 1 or 2h + l = 4n |
Symmetry of special projections
| Along [001] p4gm a' = 1/2(a - b) b' = 1/2(a + b) Origin at 0, 0, z | Along [100] c2mm a' = b b' = c Origin at x, 0, 3/8 | Along [110] c1m1 a' = 1/2(-a + b) b' = 1/2c Origin at x, x, 0 |
Maximal non-isomorphic subgroups
| I | [2] I-411 (I-4, 82) | (1; 2; 3; 4)+ | |
| [2] I21d (Fdd2, 43) | (1; 2; 7; 8)+ | ||
| [2] I221 (I212121, 24) | (1; 2; 5; 6)+ |
| IIa | none |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] I-42d (c' = 3c) (122); [9] I-42d (a' = 3a, b' = 3b) (122) |
Minimal non-isomorphic supergroups
| I | [2] I41/amd (141); [2] I41/acd (142); [3] I-43d (220) |
| II | [2] C-42d (c' = 1/2c) (P-4n2, 118) |
