ORIGIN CHOICE 1, Origin at 2 2 2, at -1/8, -1/8, -1/8 from -1
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 |
|
| | (0, 0, 0)+ (0, 1/2, 1/2)+ (1/2, 0, 1/2)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z | | (5) -x + 1/4, -y + 1/4, -z + 1/4 | (6) x + 1/4, y + 1/4, -z + 1/4 | (7) x + 1/4, -y + 1/4, z + 1/4 | (8) -x + 1/4, y + 1/4, z + 1/4 |
|
I Maximal translationengleiche subgroups
| [2] Fdd2 (43) | (1; 2; 7; 8)+ |
|
|
| [2] Fd2d (43, Fdd2) | (1; 3; 6; 8)+ | c, a, b
|
|
| [2] F2dd (43, Fdd2) | (1; 4; 6; 7)+ | b, c, a
|
|
| [2] F222 (22) | (1; 2; 3; 4)+ |
|
|
| [2] F112/d (15, A112/a) | (1; 2; 5; 6)+ | 1/2(a - b), b, c
| 1/8, 3/8, 3/8
|
| [2] F12/d1 (15, C12/c1) | (1; 3; 5; 7)+ | -c, b, 1/2(a + c)
| 1/8, 1/8, 1/8
|
| [2] F2/d11 (15, C12/c1) | (1; 4; 5; 8)+ | -b, a, 1/2(b + c)
| 1/8, 1/8, 1/8
|
II Maximal klassengleiche subgroups
- Loss of centring translations
[3] a' = 3a
 | Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 1/2); 5 + (1, 1/2, 1/2)> | 3a, b, c | 1/4, 1/4, 1/4 | | Fddd (70) | <2 + (5/2, 1/2, 0); 3 + (5/2, 0, 1/2); 5 + (3, 1/2, 1/2)> | 3a, b, c | 5/4, 1/4, 1/4 | | Fddd (70) | <2 + (9/2, 1/2, 0); 3 + (9/2, 0, 1/2); 5 + (5, 1/2, 1/2)> | 3a, b, c | 9/4, 1/4, 1/4 |
|
[3] b' = 3b
| Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 1, 1/2)> | a, 3b, c | 1/4, 1/4, 1/4 | | Fddd (70) | <2 + (1/2, 5/2, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 3, 1/2)> | a, 3b, c | 1/4, 5/4, 1/4 | | Fddd (70) | <2 + (1/2, 9/2, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 5, 1/2)> | a, 3b, c | 1/4, 9/4, 1/4 |
|
[3] c' = 3c
| Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, 1/2, 1)> | a, b, 3c | 1/4, 1/4, 1/4 | | Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 5/2); 5 + (1/2, 1/2, 3)> | a, b, 3c | 1/4, 1/4, 5/4 | | Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 9/2); 5 + (1/2, 1/2, 5)> | a, b, 3c | 1/4, 1/4, 9/4 |
|
- Series of maximal isomorphic subgroups
[p] a' = pa
| Fddd (70) | <2 + (1/2 + 2u, 1/2, 0); 3 + (1/2 + 2u, 0, 1/2); 5 + (p/4 + 1/4 + 2u, 1/2, 1/2)> | pa, b, c | 1/4 + u, 1/4, 1/4 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fddd (70) | <(2; 3) + (2u, 0, 0); 5 + (p/4 - 1/4 + 2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
|
[p] b' = pb
| Fddd (70) | <2 + (1/2, 1/2 + 2u, 0); 3 + (1/2, 0, 1/2); 5 + (1/2, p/4 + 1/4 + 2u, 1/2)> | a, pb, c | 1/4, 1/4 + u, 1/4 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fddd (70) | <3; 2 + (0, 2u, 0); 5 + (0, p/4 - 1/4 + 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 4; 0 ≤ u < p
p conjugate subgroups for prime p ≡ 1 (mod 4) |
|
[p] c' = pc
| Fddd (70) | <2 + (1/2, 1/2, 0); 3 + (1/2, 0, 1/2 + 2u); 5 + (1/2, 1/2, p/4 + 1/4 + 2u)> | a, b, pc | 1/4, 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, 2u); 5 + (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) |
|
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) |
