| I41 | C46 | 4 | Tetragonal  |
| No. 80 | I41 | Patterson symmetry I4/m | |
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2(0, 0, 1/2) 1/4, 1/4, z | (3) 4+(0, 0, 1/4) -1/4, 1/4, z | (4) 4-(0, 0, 3/4) 1/4, -1/4, z |
For (1/2, 1/2, 1/2)+ set
| (1) t(1/2, 1/2, 1/2) | (2) 2 0, 0, z | (3) 4+(0, 0, 3/4) 1/4, 1/4, z | (4) 4-(0, 0, 1/4) 1/4, 1/4, 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)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||
| (0, 0, 0)+ (1/2, 1/2, 1/2)+ | General: | ||||||||
|
| hkl : h + k + l = 2n hk0 : h + k = 2n 0kl : k + l = 2n hhl : l = 2n 00l : l = 4n h00 : h = 2n |
| Special: as above, plus | |||||||
|
| hkl : l = 2n + 1 or 2h + l = 4n |
Symmetry of special projections
| Along [001] p4 a' = 1/2(a - b) b' = 1/2(a + b) Origin at 1/4, 1/4, 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] I2 (C2, 5) | (1; 2)+ |
| IIa | [2] P43 (78) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | |
| [2] P41 (76) | 1; 2; 3; 4 |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] I41 (c' = 3c) (80); [5] I41 (a' = a + 2b, b' = -2a + b or a' = a - 2b, b' = 2a + b) (80) |
Minimal non-isomorphic supergroups
| I | [2] I41/a (88); [2] I4122 (98); [2] I41md (109); [2] I41cd (110) |
| II | [2] C42 (c' = 1/2c) (P42, 77) |
