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 |
|
I Maximal translationengleiche subgroups
| [2] I2 (5, A112) | (1; 2)+ | b, -a - b, c
|
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P42 (77) | 1; 2; (3; 4) + (1/2, 1/2, 1/2) | | 1/2, 0, 0 |
| [2] P4 (75) | 1; 2; 3; 4 | | |
[3] c' = 3c
- Series of maximal isomorphic subgroups
[p] c' = pc
| I4 (79) | <2; 3> | a, b, pc | | | | p > 2
no conjugate subgroups |
|
[p2] a' = pa, b' = pb
| I4 (79) | <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
| I4 (79) | <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) |
|
I Minimal translationengleiche supergroups
| [2] I4/m (87); [2] I422 (97); [2] I4mm (107); [2] I4cm (108) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C4 (75, P4) |
