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) y, -x, -z | (4) -y, x, -z | | (5) -x + 1/2, y, -z + 3/4 | (6) x + 1/2, -y, -z + 3/4 | (7) -y + 1/2, -x, z + 3/4 | (8) y + 1/2, x, z + 3/4 |
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I Maximal translationengleiche subgroups
| [2] I-411 (82, I-4) | (1; 2; 3; 4)+ |
|
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| [2] I21d (43, Fdd2) | (1; 2; 7; 8)+ | a - b, a + b, c
| 0, 1/2, 0
|
| [2] I221 (24, I212121) | (1; 2; 5; 6)+ |
| 0, 1/4, 3/8
|
II Maximal klassengleiche subgroups
- Loss of centring translations
[3] c' = 3c
 | I-42d (122) | <2 + (1, 0, 0); 3 + (1/2, 1/2, 1/2); 5 + (1, 0, 2)> | a, b, 3c | 1/2, 0, 1/4 | | I-42d (122) | <2 + (1, 0, 0); 3 + (1/2, 1/2, 5/2); 5 + (1, 0, 4)> | a, b, 3c | 1/2, 0, 5/4 | | I-42d (122) | <2 + (1, 0, 0); 3 + (1/2, 1/2, 9/2); 5 + (1, 0, 6)> | a, b, 3c | 1/2, 0, 9/4 |
|
- Series of maximal isomorphic subgroups
[p] c' = pc
| I-42d (122) | <2 + (1, 0, 0); 3 + (1/2, 1/2, 1/2 + u); 5 + (1, 0, 3p/4 - 1/4 + 2u)> | a, b, pc | 1/2, 0, 1/4 + u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| I-42d (122) | <2; 3; 5 + (0, 0, 3p/4 - 3/4 + 2u)> | a, b, pc | 0, 0, u | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
|
[p2] a' = pa, b' = pb
| I-42d (122) | <2 + (2u, 2v, 0); 3 + (u - v, u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] I41/amd (141); [2] I41/acd (142); [3] I-43d (220) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C-42d (118, P-4n2) |
