Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (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 |
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I Maximal translationengleiche subgroups
| [2] I2 (5, A112) | (1; 2)+ | b, -a - b, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P-4 (81) | 1; 2; 3; 4 | | |
| [2] P-4 (81) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | | 1/2, 0, 1/4 |
[3] c' = 3c
 | I-4 (82) | <2; 3> | a, b, 3c | | | I-4 (82) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | I-4 (82) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| I-4 (82) | <2; 3 + (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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[p2] a' = pa, b' = pb
| I-4 (82) | <2 + (2u, 2v, 0); 3 + (u - v, u + v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 3 (mod 4) |
|
[p = q2 + r2] a' = qa - rb, b' = ra + qb
| I-4 (82) | <2 + (2u, 0, 0); 3 + (u, u, 0)> | qa - rb, ra + qb, c | u, 0, 0 | | | q > 0; r > 0; p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
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I Minimal translationengleiche supergroups
| [2] I4/m (87); [2] I41/a (88); [2] I-4m2 (119); [2] I-4c2 (120); [2] I-42m (121); [2] I-42d (122) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C-4 (81, P-4) |
