Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z | | (5) z, x, y | (6) z, -x, -y | (7) -z, -x, y | (8) -z, x, -y | | (9) y, z, x | (10) -y, z, -x | (11) y, -z, -x | (12) -y, -z, x | | (13) y, x, -z | (14) -y, -x, -z | (15) y, -x, z | (16) -y, x, z | | (17) x, z, -y | (18) -x, z, y | (19) -x, -z, -y | (20) x, -z, y | | (21) z, y, -x | (22) z, -y, x | (23) -z, y, x | (24) -z, -y, -x |
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I Maximal translationengleiche subgroups
| [2] P231 (195, P23) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12 |
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 | [3] P412 (89, P422) | 1; 2; 3; 4; 13; 14; 15; 16 |
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| | [3] P412 (89, P422) | 1; 4; 2; 3; 18; 19; 17; 20 | b, c, a
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| | [3] P412 (89, P422) | 1; 3; 4; 2; 22; 24; 23; 21 | c, a, b
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 | [4] P132 (155, R32) | 1; 5; 9; 14; 19; 24 | a - b, b - c, a + b + c
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| | [4] P132 (155, R32) | 1; 6; 12; 13; 18; 24 | -a - b, b + c, -a + b - c
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| | [4] P132 (155, R32) | 1; 7; 10; 13; 19; 22 | a + b, -b + c, a - b - c
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| | [4] P132 (155, R32) | 1; 8; 11; 14; 18; 22 | -a + b, -b - c, -a - b + c
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II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| F432 (209) | <2; 3; 5; 13> | 2a, 2b, 2c | |
| F432 (209) | <2; 3; 5; 13 + (0, 0, 1)> | 2a, 2b, 2c | 1/2, 1/2, 1/2 |
[4] a' = 2a, b' = 2b, c' = 2c
| I432 (211) | <2; 3; 5; 13> | 2a, 2b, 2c | | | I432 (211) | <13; 2 + (2, 2, 0); 3 + (2, 0, 0); 5 + (1, 0, -1)> | 2a, 2b, 2c | 1, 1, 0 | | I432 (211) | <(2; 3) + (2, 0, 0); (5; 13) + (1, -1, 0)> | 2a, 2b, 2c | 1, 0, 0 | | I432 (211) | <3; 2 + (0, 2, 0); 5 + (0, 1, -1); 13 + (-1, 1, 0)> | 2a, 2b, 2c | 0, 1, 0 |
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| I432 (211) | <5; 2 + (1, 1, 0); 3 + (1, 0, 1); 13 + (0, 0, 1)> | 2a, 2b, 2c | 1/2, 1/2, 1/2 | | I432 (211) | <2 + (3, 3, 0); 3 + (3, 0, 1); 5 + (1, 0, -1); 13 + (0, 0, 1)> | 2a, 2b, 2c | 3/2, 3/2, 1/2 | | I432 (211) | <2 + (3, 1, 0); 3 + (3, 0, 1); 5 + (1, -1, 0); 13 + (1, -1, 1)> | 2a, 2b, 2c | 3/2, 1/2, 1/2 | | I432 (211) | <2 + (1, 3, 0); 3 + (1, 0, 1); 5 + (0, 1, -1); 13 + (-1, 1, 1)> | 2a, 2b, 2c | 1/2, 3/2, 1/2 |
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- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| P432 (207) | <2 + (2u, 2v, 0); 3 + (2u, 0, 2w); 5 + (u - w, -u + v, -v + w); 13 + (u - v, -u + v, 2w)> | pa, pb, pc | u, v, w | | | p > 2; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] Pm-3m (221); [2] Pn-3n (222) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] I432 (211); [4] F432 (209) |
