| I4mm | C4v9 | 4mm | Tetragonal  |
| No. 107 | I4mm | Patterson symmetry I4/mmm | |
Origin on 4m m
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2; x ≤ y |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2 0, 0, z | (3) 4+ 0, 0, z | (4) 4- 0, 0, z |
| (5) m x, 0, z | (6) m 0, y, z | (7) m x, -x, z | (8) m x, 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+(0, 0, 1/2) 0, 1/2, z | (4) 4-(0, 0, 1/2) 1/2, 0, z |
| (5) n(1/2, 0, 1/2) x, 1/4, z | (6) n(0, 1/2, 1/2) 1/4, y, z | (7) c x + 1/2, -x, z | (8) n(1/2, 1/2, 1/2) x, 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 : l = 2n 00l : l = 2n h00 : h = 2n |
| Special: as above, plus | |||||||||
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| no extra conditions | |||||||
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| no extra conditions | |||||||
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| hkl : l = 2n | |||||||
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| no extra conditions |
Symmetry of special projections
| Along [001] p4mm a' = 1/2(a - b) b' = 1/2(a + b) Origin at 0, 0, z | Along [100] c1m1 a' = b b' = c Origin at x, 0, 0 | Along [110] p1m1 a' = 1/2(-a + b) b' = 1/2c Origin at x, x, 0 |
Maximal non-isomorphic subgroups
| I | [2] I411 (I4, 79) | (1; 2; 3; 4)+ | |
| [2] I2m1 (Imm2, 44) | (1; 2; 5; 6)+ | ||
| [2] I21m (Fmm2, 42) | (1; 2; 7; 8)+ |
| IIa | [2] P42mc (105) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) | |
| [2] P4nc (104) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) | ||
| [2] P42nm (102) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) | ||
| [2] P4mm (99) | 1; 2; 3; 4; 5; 6; 7; 8 |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] I4mm (c' = 3c) (107); [9] I4mm (a' = 3a, b' = 3b) (107) |
Minimal non-isomorphic supergroups
| I | [2] I4/mmm (139) |
| II | [2] C4mm (c' = 1/2c) (P4mm, 99) |
