| P42bc | C4v8 | 4mm | Tetragonal  |
| No. 106 | P42bc | Patterson symmetry P4/mmm | |
Origin on 2 on 42 1 n
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
Symmetry operations
| (1) 1 | (2) 2 0, 0, z | (3) 4+(0, 0, 1/2) 0, 0, z | (4) 4-(0, 0, 1/2) 0, 0, z |
| (5) a x, 1/4, z | (6) b 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); (2); (3); (5)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||||||
| General: | |||||||||||||
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| 0kl : k = 2n hhl : l = 2n 00l : l = 2n h00 : h = 2n |
| Special: as above, plus | |||||||||
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| hkl : h + k, l = 2n | |||||||
|
| hkl : h + k, l = 2n |
Symmetry of special projections
| Along [001] p4gm a' = a b' = b Origin at 0, 0, z | Along [100] p1m1 a' = 1/2b 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] P4211 (P42, 77) | 1; 2; 3; 4 | |
| [2] P21c (Ccc2, 37) | 1; 2; 7; 8 | ||
| [2] P2b1 (Pba2, 32) | 1; 2; 5; 6 |
| IIa | none |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P42bc (c' = 3c) (106); [9] P42bc (a' = 3a, b' = 3b) (106) |
Minimal non-isomorphic supergroups
| I | [2] P42/nbc (133); [2] P42/mbc (135) |
| II | [2] C42mc (P42cm, 101); [2] I4cm (108); [2] P4bm (c' = 1/2c) (100) |
