Origin at centre (-3 m 1) at -3 2/m c
Asymmetric unit | 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 2/3; 0 ≤ z ≤ 1/4; x ≤ 2y; y ≤ min(1 - x, 2x) | ||||||
Vertices |
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Symmetry operations
(1) 1 | (2) 3+ 0, 0, z | (3) 3- 0, 0, z |
(4) 2(0, 0, 1/2) 0, 0, z | (5) 6-(0, 0, 1/2) 0, 0, z | (6) 6+(0, 0, 1/2) 0, 0, z |
(7) 2 x, x, 0 | (8) 2 x, 0, 0 | (9) 2 0, y, 0 |
(10) 2 x, -x, 1/4 | (11) 2 x, 2x, 1/4 | (12) 2 2x, x, 1/4 |
(13) -1 0, 0, 0 | (14) -3+ 0, 0, z; 0, 0, 0 | (15) -3- 0, 0, z; 0, 0, 0 |
(16) m x, y, 1/4 | (17) -6- 0, 0, z; 0, 0, 1/4 | (18) -6+ 0, 0, z; 0, 0, 1/4 |
(19) m x, -x, z | (20) m x, 2x, z | (21) m 2x, x, z |
(22) c x, x, z | (23) c x, 0, z | (24) c 0, y, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4); (7); (13)
Positions
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||||||||||||||||||||||
General: | |||||||||||||||||||||||||||||
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| hh(-2h)l : l = 2n 000l : l = 2n |
Special: as above, plus | |||||||||||||||||
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| no extra conditions | |||||||||||||||
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| no extra conditions | |||||||||||||||
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| hkil : l = 2n | |||||||||||||||
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| no extra conditions | |||||||||||||||
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| hkil : l = 2n | |||||||||||||||
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| hkil : l = 2n or h - k = 3n + 1 or h - k = 3n + 2 | |||||||||||||||
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| hkil : l = 2n | |||||||||||||||
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| hkil : l = 2n or h - k = 3n + 1 or h - k = 3n + 2 | |||||||||||||||
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| hkil : l = 2n | |||||||||||||||
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| hkil : l = 2n |
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] p2mm a' = 1/2b b' = 1/2c Origin at x, 1/2x, 0 |
Maximal non-isomorphic subgroups
I | [2] P-62c (190) | 1; 2; 3; 7; 8; 9; 16; 17; 18; 22; 23; 24 | |||||||||||
[2] P-6m2 (187) | 1; 2; 3; 10; 11; 12; 16; 17; 18; 19; 20; 21 | ||||||||||||
[2] P63mc (186) | 1; 2; 3; 4; 5; 6; 19; 20; 21; 22; 23; 24 | ||||||||||||
[2] P6322 (182) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12 | ||||||||||||
[2] P63/m11 (P63/m, 176) | 1; 2; 3; 4; 5; 6; 13; 14; 15; 16; 17; 18 | ||||||||||||
[2] P-3m1 (164) | 1; 2; 3; 7; 8; 9; 13; 14; 15; 19; 20; 21 | ||||||||||||
[2] P-31c (163) | 1; 2; 3; 10; 11; 12; 13; 14; 15; 22; 23; 24 | ||||||||||||
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IIa | none |
IIb | [3] H63/mmc (a' = 3a, b' = 3b) (P63/mcm, 193) |
Maximal isomorphic subgroups of lowest index
IIc | [3] P63/mmc (c' = 3c) (194); [4] P63/mmc (a' = 2a, b' = 2b) (194) |
Minimal non-isomorphic supergroups
I | none |
II | [3] H63/mmc (P63/mcm, 193); [2] P6/mmm (c' = 1/2c) (191) |