ORIGIN CHOICE 1, Origin at -4c 21, at 0, 1/4, -1/8 from -1
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); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z + 1/2 | (3) -y, x + 1/2, z + 1/4 | (4) y + 1/2, -x, z + 3/4 | | (5) -x + 1/2, y, -z + 1/4 | (6) x, -y + 1/2, -z + 3/4 | (7) y + 1/2, x + 1/2, -z | (8) -y, -x, -z + 1/2 | | (9) -x, -y + 1/2, -z + 1/4 | (10) x + 1/2, y, -z + 3/4 | (11) y, -x, -z | (12) -y + 1/2, x + 1/2, -z + 1/2 | | (13) x + 1/2, -y + 1/2, z | (14) -x, y, z + 1/2 | (15) -y + 1/2, -x, z + 1/4 | (16) y, x + 1/2, z + 3/4 |
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I Maximal translationengleiche subgroups
| [2] I-42d (122) | (1; 2; 5; 6; 11; 12; 15; 16)+ |
| 0, 1/2, 1/4
|
| [2] I-4c2 (120) | (1; 2; 7; 8; 11; 12; 13; 14)+ |
|
|
| [2] I41cd (110) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
|
|
| [2] I4122 (98) | (1; 2; 3; 4; 5; 6; 7; 8)+ |
| 0, 0, 1/4
|
| [2] I41/a11 (88, I41/a) | (1; 2; 3; 4; 9; 10; 11; 12)+ |
|
|
| [2] I2/a2/c1 (73, Ibca) | (1; 2; 5; 6; 9; 10; 13; 14)+ |
| 0, 1/4, 1/8
|
| [2] I2/a12/d (70, Fddd) | (1; 2; 7; 8; 9; 10; 15; 16)+ | a - b, a + b, c
| 0, 0, 1/4
|
II Maximal klassengleiche subgroups
- Loss of centring translations
[3] c' = 3c
 | I41/acd (142) | <(2; 5; 9) + (1, 0, 1); 3 + (1/2, -1/2, 1/2)> | a, b, 3c | 1/2, 0, 1/4 | | I41/acd (142) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2); (5; 9) + (1, 0, 3)> | a, b, 3c | 1/2, 0, 5/4 | | I41/acd (142) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2); (5; 9) + (1, 0, 5)> | a, b, 3c | 1/2, 0, 9/4 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| I41/acd (142) | <2 + (1, 0, p/2 - 1/2); 3 + (1/2, -1/2, p/4 - 1/4); (5; 9) + (1, 0, p/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) |
| I41/acd (142) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/4 - 1/4); (5; 9) + (0, 0, p/4 - 1/4 + 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
| I41/acd (142) | <2 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0); 3 + (u + v, p/2 - 1/2 - u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 0); 9 + (2u, p/2 - 1/2 + 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
|
I Minimal translationengleiche supergroups
| [3] Fd-3c (228); [3] Ia-3d (230) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C42/emd (134, P42/nnm) |
ORIGIN CHOICE 2, Origin at -1 at b (c, a) d, at 0, -1/4, 1/8 from -4
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); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y, z + 1/2 | (3) -y + 1/4, x + 3/4, z + 1/4 | (4) y + 1/4, -x + 1/4, z + 3/4 | | (5) -x + 1/2, y, -z | (6) x, -y, -z + 1/2 | (7) y + 1/4, x + 3/4, -z + 3/4 | (8) -y + 1/4, -x + 1/4, -z + 1/4 | | (9) -x, -y, -z | (10) x + 1/2, y, -z + 1/2 | (11) y + 3/4, -x + 1/4, -z + 3/4 | (12) -y + 3/4, x + 3/4, -z + 1/4 | | (13) x + 1/2, -y, z | (14) -x, y, z + 1/2 | (15) -y + 3/4, -x + 1/4, z + 1/4 | (16) y + 3/4, x + 3/4, z + 3/4 |
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I Maximal translationengleiche subgroups
| [2] I-42d (122) | (1; 2; 5; 6; 11; 12; 15; 16)+ |
| 0, 3/4, 1/8
|
| [2] I-4c2 (120) | (1; 2; 7; 8; 11; 12; 13; 14)+ |
| 0, 1/4, 3/8
|
| [2] I41cd (110) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
| 0, 1/4, 0
|
| [2] I4122 (98) | (1; 2; 3; 4; 5; 6; 7; 8)+ |
| 0, 1/4, 1/8
|
| [2] I41/a11 (88, I41/a) | (1; 2; 3; 4; 9; 10; 11; 12)+ |
| 0, 1/2, 0
|
| [2] I2/a2/c1 (73, Ibca) | (1; 2; 5; 6; 9; 10; 13; 14)+ |
|
|
| [2] I2/a12/d (70, Fddd) | (1; 2; 7; 8; 9; 10; 15; 16)+ | a - b, a + b, c
| 1/4, 1/4, 1/4
|
II Maximal klassengleiche subgroups
- Loss of centring translations
[3] c' = 3c
| I41/acd (142) | <5; 9; 2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2)> | a, b, 3c | 1/2, 0, 0 | | I41/acd (142) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2); (5; 9) + (0, 0, 2)> | a, b, 3c | 1/2, 0, 1 | | I41/acd (142) | <2 + (1, 0, 1); 3 + (1/2, -1/2, 1/2); (5; 9) + (0, 0, 4)> | a, b, 3c | 1/2, 0, 2 |
|
- Series of maximal isomorphic subgroups
[p] c' = pc
| I41/acd (142) | <2 + (1, 0, p/2 - 1/2); 3 + (1/2, -1/2, p/4 - 1/4); (5; 9) + (1, 0, 2u)> | a, b, pc | 1/2, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| I41/acd (142) | <2 + (0, 0, p/2 - 1/2); 3 + (0, 0, p/4 - 1/4); (5; 9) + (0, 0, 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
| I41/acd (142) | <2 + (p/2 + 1/2 + 2u, 2v, 0); 3 + (p/4 + 1/4 + u + v, 3p/4 + 5/4 - u + v, 0); 5 + (p/2 + 1/2 + 2u, 0, 0); 9 + (1 + 2u, 2v, 0)> | pa, pb, c | 1/2 + u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 3 (mod 4) |
| I41/acd (142) | <2 + (p/2 - 1/2 + 2u, 2v, 0); 3 + (p/4 - 1/4 + u + v, 3p/4 - 3/4 - u + v, 0); 5 + (p/2 - 1/2 + 2u, 0, 0); 9 + (2u, 2v, 0)> | pa, pb, c | u, v, 0 | | | p > 4; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 1 (mod 4) |
|
I Minimal translationengleiche supergroups
| [3] Fd-3c (228); [3] Ia-3d (230) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C42/emd (134, P42/nnm) |
