Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); t(1/2, 0, 1/2); (2); (3); (5); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (0, 1/2, 1/2)+ (1/2, 0, 1/2)+ (1/2, 1/2, 0)+ |
| | (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] F231 (196, F23) | (1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12)+ |
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 | [3] F-41m (119, I-4m2) | (1; 2; 3; 4; 13; 14; 15; 16)+ | 1/2(a - b), 1/2(a + b), c
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| | [3] F-41m (119, I-4m2) | (1; 4; 2; 3; 17; 20; 18; 19)+ | 1/2(b - c), 1/2(b + c), a
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| | [3] F-41m (119, I-4m2) | (1; 3; 4; 2; 21; 23; 24; 22)+ | 1/2(-a + c), 1/2(a + c), b
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 | [4] F13m (160, R3m) | (1; 5; 9; 13; 17; 21)+ | 1/2(-a + b), 1/2(-b + c), a + b + c
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| | [4] F13m (160, R3m) | (1; 6; 12; 14; 20; 21)+ | 1/2(a + b), 1/2(-b - c), -a + b - c
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| | [4] F13m (160, R3m) | (1; 7; 10; 14; 17; 23)+ | 1/2(-a - b), 1/2(b - c), a - b - c
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| | [4] F13m (160, R3m) | (1; 8; 11; 13; 20; 23)+ | 1/2(a - b), 1/2(b + c), -a - b + c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [4] 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 | | | | [4] P-43m (215) | 1; 2; 3; 4; 13; 14; 15; 16; (5; 6; 7; 8; 21; 22; 23; 24) + (1/2, 0, 1/2); (9; 10; 11; 12; 17; 18; 19; 20) + (0, 1/2, 1/2) | | 1/2, 1/2, 0 | | [4] P-43m (215) | 1; 2; 3; 4; 17; 18; 19; 20; (5; 6; 7; 8; 13; 14; 15; 16) + (1/2, 1/2, 0); (9; 10; 11; 12; 21; 22; 23; 24) + (1/2, 0, 1/2) | | 0, 1/2, 1/2 | | [4] P-43m (215) | 1; 2; 3; 4; 21; 22; 23; 24; (5; 6; 7; 8; 17; 18; 19; 20) + (0, 1/2, 1/2); (9; 10; 11; 12; 13; 14; 15; 16) + (1/2, 1/2, 0) | | 1/2, 0, 1/2 |
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| [4] P-43m (215) | 1; 5; 9; 13; 17; 21; (2; 7; 12; 14; 19; 24) + (1/2, 1/2, 0); (3; 8; 10; 16; 18; 23) + (1/2, 0, 1/2); (4; 6; 11; 15; 20; 22) + (0, 1/2, 1/2) | | 1/4, 1/4, 1/4 | | [4] P-43m (215) | 1; 6; 12; 14; 20; 21; (2; 8; 9; 13; 18; 24) + (1/2, 1/2, 0); (3; 7; 11; 15; 19; 23) + (1/2, 0, 1/2); (4; 5; 10; 16; 17; 22) + (0, 1/2, 1/2) | | 3/4, 1/4, 3/4 | | [4] P-43m (215) | 1; 7; 10; 14; 17; 23; (2; 5; 11; 13; 19; 22) + (1/2, 1/2, 0); (3; 6; 9; 15; 18; 21) + (1/2, 0, 1/2); (4; 8; 12; 16; 20; 24) + (0, 1/2, 1/2) | | 1/4, 3/4, 3/4 | | [4] P-43m (215) | 1; 8; 11; 13; 20; 23; (2; 6; 10; 14; 18; 22) + (1/2, 1/2, 0); (3; 5; 12; 16; 19; 21) + (1/2, 0, 1/2); (4; 7; 9; 15; 17; 24) + (0, 1/2, 1/2) | | 3/4, 3/4, 1/4 |
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- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| F-43m (216) | <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
| [2] Fm-3m (225); [2] Fd-3m (227) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c P-43m (215) |
