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)
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 + 1/2, y + 1/2, -z | (4) x + 1/2, -y + 1/2, -z | | (5) -x, -y, -z | (6) x, y, -z | (7) x + 1/2, -y + 1/2, z | (8) -x + 1/2, y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] Ib2m (46, Ima2) | (1; 3; 6; 8)+ | c, a, b
| 0, 0, 1/4
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| [2] I2am (46, Ima2) | (1; 4; 6; 7)+ | c, b, -a
| 0, 0, 1/4
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| [2] Iba2 (45) | (1; 2; 7; 8)+ |
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| [2] I222 (23) | (1; 2; 3; 4)+ |
| 0, 0, 1/4
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| [2] I12/a1 (15, C12/c1) | (1; 3; 5; 7)+ | a - c, b, c
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| [2] I2/b11 (15, C12/c1) | (1; 4; 5; 8)+ | -b - c, a, c
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| [2] I112/m (12, A112/m) | (1; 2; 5; 6)+ | b, -a - b, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pcan (60, Pbcn) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 1/2) | -b, a, c | |
| [2] Pbcn (60) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 1/2) | | |
| [2] Pbcm (57) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] Pcam (57, Pbcm) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 1/2) | -b, a, c | 1/4, 1/4, 1/4 |
| [2] Pccn (56) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] Pbam (55) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
| [2] Pban (50) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] Pccm (49) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 1/2) | | |
[3] a' = 3a
 | Ibam (72) | <2; 5; 3 + (1, 0, 0)> | 3a, b, c | | | Ibam (72) | <(2; 5) + (2, 0, 0); 3 + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | Ibam (72) | <(2; 5) + (4, 0, 0); 3 + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Ibam (72) | <2; 5; 3 + (0, 1, 0)> | a, 3b, c | | | Ibam (72) | <(2; 5) + (0, 2, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 1, 0 | | Ibam (72) | <(2; 5) + (0, 4, 0); 3 + (0, 1, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Ibam (72) | <2; 3; 5> | a, b, 3c | | | Ibam (72) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Ibam (72) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Ibam (72) | <(2; 5) + (2u, 0, 0); 3 + (p/2 - 1/2 + 2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] b' = pb
| Ibam (72) | <(2; 5) + (0, 2u, 0); 3 + (0, p/2 - 1/2, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| Ibam (72) | <2; (3; 5) + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c Cmmm (65); [2] a' = 1/2a Aemm (67, Cmme); [2] b' = 1/2b Bmem (67, Cmme) |
