| I41/a | C4h6 | 4/m | Tetragonal  |
| No. 88 | I41/a | Patterson symmetry I4/m | |
| ORIGIN CHOICE 2 | |||
Origin at -1 on glide plane b, at 0, 1/4, 1/8 from -4
| 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, 1/2) 1/4, 0, z | (3) 4+(0, 0, 1/4) 1/4, 1/2, z | (4) 4-(0, 0, 3/4) 3/4, 0, z |
| (5) -1 0, 0, 0 | (6) a x, y, 1/4 | (7) -4+ 1/2, 1/4, z; 1/2, 1/4, 3/8 | (8) -4- 0, 1/4, z; 0, 1/4, 1/8 |
For (1/2, 1/2, 1/2)+ set
| (1) t(1/2, 1/2, 1/2) | (2) 2 0, 1/4, z | (3) 4+(0, 0, 3/4) -1/4, 1/2, z | (4) 4-(0, 0, 1/4) 1/4, 0, z |
| (5) -1 1/4, 1/4, 1/4 | (6) b x, y, 0 | (7) -4+ 1/2, -1/4, z; 1/2, -1/4, 1/8 | (8) -4- 0, 3/4, z; 0, 3/4, 3/8 |
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 = 4n h00 : h = 2n h-h0 : h = 2n |
| Special: as above, plus | |||||||||
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| hkl : l = 2n + 1 or 2h + l = 4n | |||||||
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| hkl : l = 2n + 1 or h, k = 2n, h + k + l = 4n | |||||||
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| hkl : l = 2n + 1 or 2h + l = 4n | |||||||
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Symmetry of special projections
| Along [001] p4 a' = 1/2a b' = 1/2b Origin at 1/4, 0, z | Along [100] c2mm a' = b b' = c Origin at x, 1/4, 1/4 | Along [110] p2mg a' = 1/2(-a + b) b' = 1/2c Origin at x, x, 0 |
Maximal non-isomorphic subgroups
| I | [2] I-4 (82) | (1; 2; 7; 8)+ | |
| [2] I41 (80) | (1; 2; 3; 4)+ | ||
| [2] I2/a (C2/c, 15) | (1; 2; 5; 6)+ |
| IIa | none |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] I41/a (c' = 3c) (88); [5] I41/a (a' = a + 2b, b' = -2a + b or a' = a - 2b, b' = 2a + b) (88) |
Minimal non-isomorphic supergroups
| I | [2] I41/amd (141); [2] I41/acd (142) |
| II | [2] C42/a (c' = 1/2c) (P42/n, 86) |
