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); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (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] I231 (197, I23) | (1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12)+ |
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 | [3] I-41m (121, I-42m) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
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| | [3] I-41m (121, I-42m) | (1; 4; 2; 3; 17; 20; 18; 19)+ | b, c, a
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| | [3] I-41m (121, I-42m) | (1; 3; 4; 2; 21; 23; 24; 22)+ | c, a, b
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 | [4] I13m (160, R3m) | (1; 5; 9; 13; 17; 21)+ | -a + b, -b + c, 1/2(a + b + c)
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| | [4] I13m (160, R3m) | (1; 6; 12; 14; 20; 21)+ | a + b, -b - c, 1/2(-a + b - c)
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| | [4] I13m (160, R3m) | (1; 7; 10; 14; 17; 23)+ | -a - b, b - c, 1/2(a - b - c)
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| | [4] I13m (160, R3m) | (1; 8; 11; 13; 20; 23)+ | a - b, b + c, 1/2(-a - b + c)
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P-43n (218) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; (13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24) + (1/2, 1/2, 1/2) | | |
| [2] P-43m (215) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24 | | |
- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| I-43m (217) | <2 + (2u, 2v, 0); 3 + (2u, 0, 2w); 5 + (u - w, -u + v, -v + w); 13 + (u - v, -u + v, 0)> | 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
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [4] a' = 1/2a, b' = 1/2b, c' = 1/2c P-43m (215) |
