ORIGIN CHOICE 2, Origin at -1 at d d d, at 1/8, 1/8, 1/8 from 2 2 2
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)
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 + 3/4, -y + 3/4, z | (3) -x + 3/4, y, -z + 3/4 | (4) x, -y + 3/4, -z + 3/4 | | (5) -x, -y, -z | (6) x + 1/4, y + 1/4, -z | (7) x + 1/4, -y, z + 1/4 | (8) -x, y + 1/4, z + 1/4 |
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I Maximal translationengleiche subgroups
| [2] Fdd2 (43) | (1; 2; 7; 8)+ |
| 3/8, 3/8, 0
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| [2] Fd2d (43, Fdd2) | (1; 3; 6; 8)+ | c, a, b
| 3/8, 0, 3/8
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| [2] F2dd (43, Fdd2) | (1; 4; 6; 7)+ | b, c, a
| 0, 3/8, 3/8
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| [2] F222 (22) | (1; 2; 3; 4)+ |
| 1/8, 1/8, 1/8
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| [2] F112/d (15, A112/a) | (1; 2; 5; 6)+ | 1/2(a - b), b, c
| 0, 1/4, 1/4
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| [2] F12/d1 (15, C12/c1) | (1; 3; 5; 7)+ | -c, b, 1/2(a + c)
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| [2] F2/d11 (15, C12/c1) | (1; 4; 5; 8)+ | -b, a, 1/2(b + c)
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II Maximal klassengleiche subgroups
- Loss of centring translations
[3] a' = 3a
 | Fddd (70) | <2 + (3/2, 1/2, 0); 3 + (3/2, 0, 1/2); 5 + (0, 1/2, 1/2)> | 3a, b, c | 0, 1/4, 1/4 | | Fddd (70) | <2 + (7/2, 1/2, 0); 3 + (7/2, 0, 1/2); 5 + (2, 1/2, 1/2)> | 3a, b, c | 1, 1/4, 1/4 | | Fddd (70) | <2 + (11/2, 1/2, 0); 3 + (11/2, 0, 1/2); 5 + (4, 1/2, 1/2)> | 3a, b, c | 2, 1/4, 1/4 |
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[3] b' = 3b
| Fddd (70) | <2 + (1/2, 3/2, 0); (3; 5) + (1/2, 0, 1/2)> | a, 3b, c | 1/4, 0, 1/4 | | Fddd (70) | <2 + (1/2, 7/2, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 2, 1/2)> | a, 3b, c | 1/4, 1, 1/4 | | Fddd (70) | <2 + (1/2, 11/2, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 4, 1/2)> | a, 3b, c | 1/4, 2, 1/4 |
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[3] c' = 3c
| Fddd (70) | <(2; 5) + (1/2, 1/2, 0); 3 + (1/2, 0, 3/2)> | a, b, 3c | 1/4, 1/4, 0 | | Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 7/2); 5 + (1/2, 1/2, 2)> | a, b, 3c | 1/4, 1/4, 1 | | Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 11/2); 5 + (1/2, 1/2, 4)> | a, b, 3c | 1/4, 1/4, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Fddd (70) | <2 + (3p/4 - 3/4 + 2u, 1/2, 0); 3 + (3p/4 - 3/4 + 2u, 0, 1/2); 5 + (2u, 1/2, 1/2)> | pa, b, c | u, 1/4, 1/4 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fddd (70) | <(2; 3) + (3p/4 - 3/4 + 2u, 0, 0); 5 + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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[p] b' = pb
| Fddd (70) | <2 + (1/2, 3p/4 - 3/4 + 2u, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 2u, 1/2)> | a, pb, c | 1/4, u, 1/4 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fddd (70) | <3; 2 + (0, 3p/4 - 3/4 + 2u, 0); 5 + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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[p] c' = pc
| Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 3p/4 - 3/4 + 2u); 5 + (1/2, 1/2, 2u)> | a, b, pc | 1/4, 1/4, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fddd (70) | <2; 3 + (0, 0, 3p/4 - 3/4 + 2u); 5 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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I Minimal translationengleiche supergroups
| [2] I41/amd (141); [2] I41/acd (142); [3] Fd-3 (203) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c Pnnn (48) |
