| P6122 | D62 | 622 | Hexagonal  |
| No. 178 | P6122 | Patterson symmetry P6/mmm | |
Origin on 2[1 0 0] at 61 (2, 1, 1) 1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/12 | ||||||||
| Vertices |
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Symmetry operations
| (1) 1 | (2) 3+(0, 0, 1/3) 0, 0, z | (3) 3-(0, 0, 2/3) 0, 0, z |
| (4) 2(0, 0, 1/2) 0, 0, z | (5) 6-(0, 0, 5/6) 0, 0, z | (6) 6+(0, 0, 1/6) 0, 0, z |
| (7) 2 x, x, 1/6 | (8) 2 x, 0, 0 | (9) 2 0, y, 1/3 |
| (10) 2 x, -x, 5/12 | (11) 2 x, 2x, 1/4 | (12) 2 2x, x, 1/12 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4); (7)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||||||||||
| General: | |||||||||||||||||
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| 000l : l = 6n |
| Special: as above, plus | |||||||||||
|
| hh(-2h)l : l = 2n or l = 3n + 1 or l = 3n + 2 | |||||||||
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| h-h0l : l = 2n or l = 3n + 1 or l = 3n + 2 |
Symmetry of special projections
| Along [001] p6mm a' = a b' = b Origin at 0, 0, z | Along [100] p2gm a' = 1/2(a + 2b) b' = c Origin at x, 0, 0 | Along [210] p2gm a' = 1/2b b' = c Origin at x, 1/2x, 1/12 |
Maximal non-isomorphic subgroups
| I | [2] P6111 (P61, 169) | 1; 2; 3; 4; 5; 6 | |||||||||||
| [2] P3121 (152) | 1; 2; 3; 7; 8; 9 | ||||||||||||
| [2] P3112 (151) | 1; 2; 3; 10; 11; 12 | ||||||||||||
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![[brace]](/graphics/sg/brace3.gif)
| IIa | none |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [3] H6122 (a' = 3a, b' = 3b) (P6122, 178); [5] P6522 (c' = 5c) (179); [7] P6122 (c' = 7c) (178) |
Minimal non-isomorphic supergroups
| I | none |
| II | [2] P6222 (c' = 1/2c) (180); [3] P6322 (c' = 1/3c) (182) |
