ORIGIN CHOICE 1, Origin at 2 2 2 at 2/n 2/n 2, at 0, 1/4, 1/4 from -1
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z | (3) -x, y, -z | (4) x + 1/2, -y + 1/2, -z | | (5) -x, -y + 1/2, -z + 1/2 | (6) x + 1/2, y, -z + 1/2 | (7) x, -y + 1/2, z + 1/2 | (8) -x + 1/2, y, z + 1/2 |
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I Maximal translationengleiche subgroups
| [2] Cc2e (41, Aea2) | (1; 3; 6; 8)+ | c, a, b
|
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| [2] C2ce (41, Aea2) | (1; 4; 6; 7)+ | c, b, -a
|
|
| [2] Ccc2 (37) | (1; 2; 7; 8)+ |
| 1/4, 1/4, 0
|
| [2] C222 (21) | (1; 2; 3; 4)+ |
|
|
| [2] C12/c1 (15) | (1; 3; 5; 7)+ |
| 0, 1/4, 1/4
|
| [2] C2/c11 (15, C12/c1) | (1; 4; 5; 8)+ | -b, a, c
| 1/4, 0, 1/4
|
| [2] C112/e (13, P112/a) | (1; 2; 5; 6)+ | a, 1/2(-a + b), c
| 1/4, 0, 1/4
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pcnb (60, Pbcn) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 0) | a, -c, b | 0, 1/4, 1/4 |
| [2] Pnca (60, Pbcn) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 0) | b, c, a | 1/4, 0, 1/4 |
| [2] Pcca (54) | 1; 2; 3; 4; 5; 6; 7; 8 | | 0, 1/4, 1/4 |
| [2] Pccb (54, Pcca) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 0) | -b, a, c | 1/4, 0, 1/4 |
| [2] Pnnb (52, Pnna) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 0) | -b, a, c | 1/4, 0, 1/4 |
| [2] Pnna (52) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 0) | | 0, 1/4, 1/4 |
| [2] Pncb (50, Pban) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 0) | b, c, a | |
| [2] Pcna (50, Pban) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 0) | c, a, b | |
[3] a' = 3a
 | Ccce (68) | <3; 5; 2 + (1, 0, 0)> | 3a, b, c | | | Ccce (68) | <2 + (3, 0, 0); (3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Ccce (68) | <2 + (5, 0, 0); (3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Ccce (68) | <3; (2; 5) + (0, 1, 0)> | a, 3b, c | | | Ccce (68) | <3; (2; 5) + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Ccce (68) | <3; (2; 5) + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Ccce (68) | <2; 3; 5 + (0, 0, 1)> | a, b, 3c | | | Ccce (68) | <2; 3 + (0, 0, 2); 5 + (0, 0, 3)> | a, b, 3c | 0, 0, 1 | | Ccce (68) | <2; 3 + (0, 0, 4); 5 + (0, 0, 5)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Ccce (68) | <2 + (p/2 - 1/2 + 2u, 0, 0); (3; 5) + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] b' = pb
| Ccce (68) | <3; (2; 5) + (0, p/2 - 1/2 + 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| Ccce (68) | <2; 3 + (0, 0, 2u); 5 + (0, 0, p/2 - 1/2 + 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P4/nnc (126); [2] P4/ncc (130); [2] P42/nbc (133); [2] P42/nmc (137) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b Pccm (49); [2] c' = 1/2c Cmme (67) |
ORIGIN CHOICE 2, Origin at -1 at 2/n c a, at 0, -1/4, -1/4 from 2 2 2
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | (0, 0, 0)+ (1/2, 1/2, 0)+ |
| | (1) x, y, z | (2) -x + 1/2, -y, z | (3) -x, y, -z + 1/2 | (4) x + 1/2, -y, -z + 1/2 | | (5) -x, -y, -z | (6) x + 1/2, y, -z | (7) x, -y, z + 1/2 | (8) -x + 1/2, y, z + 1/2 |
|
I Maximal translationengleiche subgroups
| [2] Cc2e (41, Aea2) | (1; 3; 6; 8)+ | c, a, b
| 0, 1/4, 1/4
|
| [2] C2ce (41, Aea2) | (1; 4; 6; 7)+ | c, b, -a
| 0, 1/4, 1/4
|
| [2] Ccc2 (37) | (1; 2; 7; 8)+ |
| 1/4, 0, 1/4
|
| [2] C222 (21) | (1; 2; 3; 4)+ |
| 0, 1/4, 1/4
|
| [2] C12/c1 (15) | (1; 3; 5; 7)+ |
|
|
| [2] C2/c11 (15, C12/c1) | (1; 4; 5; 8)+ | -b, a, c
| 1/4, 1/4, 0
|
| [2] C112/e (13, P112/a) | (1; 2; 5; 6)+ | a, 1/2(-a + b), c
| 1/4, 1/4, 0
|
II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] Pcnb (60, Pbcn) | 1; 4; 5; 8; (2; 3; 6; 7) + (1/2, 1/2, 0) | a, -c, b | |
| [2] Pnca (60, Pbcn) | 1; 4; 6; 7; (2; 3; 5; 8) + (1/2, 1/2, 0) | b, c, a | 1/4, 1/4, 0 |
| [2] Pcca (54) | 1; 2; 3; 4; 5; 6; 7; 8 | | |
| [2] Pccb (54, Pcca) | 1; 2; 7; 8; (3; 4; 5; 6) + (1/2, 1/2, 0) | -b, a, c | 1/4, 1/4, 0 |
| [2] Pnnb (52, Pnna) | 1; 2; 3; 4; (5; 6; 7; 8) + (1/2, 1/2, 0) | -b, a, c | 1/4, 1/4, 0 |
| [2] Pnna (52) | 1; 2; 5; 6; (3; 4; 7; 8) + (1/2, 1/2, 0) | | |
| [2] Pncb (50, Pban) | 1; 3; 5; 7; (2; 4; 6; 8) + (1/2, 1/2, 0) | b, c, a | |
| [2] Pcna (50, Pban) | 1; 3; 6; 8; (2; 4; 5; 7) + (1/2, 1/2, 0) | c, a, b | 1/4, 1/4, 0 |
[3] a' = 3a
| Ccce (68) | <3; 5; 2 + (1, 0, 0)> | 3a, b, c | | | Ccce (68) | <2 + (3, 0, 0); (3; 5) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Ccce (68) | <2 + (5, 0, 0); (3; 5) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Ccce (68) | <2; 3; 5> | a, 3b, c | | | Ccce (68) | <3; (2; 5) + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Ccce (68) | <3; (2; 5) + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Ccce (68) | <2; 5; 3 + (0, 0, 1)> | a, b, 3c | | | Ccce (68) | <2; 3 + (0, 0, 3); 5 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Ccce (68) | <2; 3 + (0, 0, 5); 5 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Ccce (68) | <2 + (p/2 - 1/2 + 2u, 0, 0); (3; 5) + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
[p] b' = pb
| Ccce (68) | <3; (2; 5) + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| Ccce (68) | <2; 3 + (0, 0, p/2 - 1/2 + 2u); 5 + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
|
I Minimal translationengleiche supergroups
| [2] P4/nnc (126); [2] P4/ncc (130); [2] P42/nbc (133); [2] P42/nmc (137) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b Pccm (49); [2] c' = 1/2c Cmme (67) |
