ORIGIN CHOICE 1, Origin at 2 2 2/n, at 1/4, 1/4, 0 from -1
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | |
| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z | | (5) -x + 1/2, -y + 1/2, -z | (6) x + 1/2, y + 1/2, -z | (7) x + 1/2, -y + 1/2, z | (8) -x + 1/2, y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] Pba2 (32) | 1; 2; 7; 8 |
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| [2] Pb2n (30, Pnc2) | 1; 3; 6; 8 | c, a, b
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| [2] P2an (30, Pnc2) | 1; 4; 6; 7 | c, b, -a
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| [2] P222 (16) | 1; 2; 3; 4 |
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| [2] P112/n (13, P112/a) | 1; 2; 5; 6 | -a - b, a, c
| 1/4, 1/4, 0
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| [2] P12/a1 (13, P12/c1) | 1; 3; 5; 7 | -a - c, b, a
| 1/4, 1/4, 0
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| [2] P2/b11 (13, P12/c1) | 1; 4; 5; 8 | c, a, b
| 1/4, 1/4, 0
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II Maximal klassengleiche subgroups
[2] c' = 2c
| Pnan (52, Pnna) | <3; 5; 2 + (0, 0, 1)> | a, -2c, b | 1/4, 1/4, 0 |
| Pnan (52, Pnna) | <(2; 3; 5) + (0, 0, 1)> | a, -2c, b | 1/4, 1/4, 1/2 |
| Pbnn (52, Pnna) | <5; (2; 3) + (0, 0, 1)> | b, 2c, a | 1/4, 1/4, 0 |
| Pbnn (52, Pnna) | <3; (2; 5) + (0, 0, 1)> | b, 2c, a | 1/4, 1/4, 1/2 |
| Pban (50) | <2; 3; 5> | a, b, 2c | |
| Pban (50) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pnnn (48) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pnnn (48) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | |
[3] a' = 3a
 | Pban (50) | <2; 3; 5 + (1, 0, 0)> | 3a, b, c | | | Pban (50) | <(2; 3) + (2, 0, 0); 5 + (3, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pban (50) | <(2; 3) + (4, 0, 0); 5 + (5, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pban (50) | <2; 3; 5 + (0, 1, 0)> | a, 3b, c | | | Pban (50) | <3; 2 + (0, 2, 0); 5 + (0, 3, 0)> | a, 3b, c | 0, 1, 0 | | Pban (50) | <3; 2 + (0, 4, 0); 5 + (0, 5, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pban (50) | <2; 3; 5> | a, b, 3c | | | Pban (50) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pban (50) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pban (50) | <(2; 3) + (2u, 0, 0); 5 + (p/2 - 1/2 + 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
| Pban (50) | <3; 2 + (0, 2u, 0); 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
| Pban (50) | <2; (3; 5) + (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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I Minimal translationengleiche supergroups
| [2] P4/nbm (125); [2] P42/nbc (133) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Cmmm (65); [2] Aeaa (68, Ccce); [2] Bbeb (68, Ccce); [2] Ibam (72) |
| [2] a' = 1/2a Pbmb (49, Pccm); [2] b' = 1/2b Pmaa (49, Pccm) |
ORIGIN CHOICE 2, Origin at -1 at b a n, at -1/4, -1/4, 0 from 2 2 2
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z | (3) -x + 1/2, y, -z | (4) x, -y + 1/2, -z | | (5) -x, -y, -z | (6) x + 1/2, y + 1/2, -z | (7) x + 1/2, -y, z | (8) -x, y + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] Pba2 (32) | 1; 2; 7; 8 |
| 1/4, 1/4, 0
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| [2] Pb2n (30, Pnc2) | 1; 3; 6; 8 | c, a, b
| 1/4, 1/4, 0
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| [2] P2an (30, Pnc2) | 1; 4; 6; 7 | c, b, -a
| 1/4, 1/4, 0
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| [2] P222 (16) | 1; 2; 3; 4 |
| 1/4, 1/4, 0
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| [2] P112/n (13, P112/a) | 1; 2; 5; 6 | -a - b, a, c
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| [2] P12/a1 (13, P12/c1) | 1; 3; 5; 7 | -a - c, b, a
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| [2] P2/b11 (13, P12/c1) | 1; 4; 5; 8 | c, a, b
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II Maximal klassengleiche subgroups
[2] c' = 2c
| Pnan (52, Pnna) | <3; 5; 2 + (0, 0, 1)> | a, -2c, b | |
| Pnan (52, Pnna) | <(2; 3; 5) + (0, 0, 1)> | a, -2c, b | 0, 0, 1/2 |
| Pbnn (52, Pnna) | <5; (2; 3) + (0, 0, 1)> | b, 2c, a | |
| Pbnn (52, Pnna) | <3; (2; 5) + (0, 0, 1)> | b, 2c, a | 0, 0, 1/2 |
| Pban (50) | <2; 3; 5> | a, b, 2c | |
| Pban (50) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| Pnnn (48) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | |
| Pnnn (48) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] a' = 3a
| Pban (50) | <5; (2; 3) + (1, 0, 0)> | 3a, b, c | | | Pban (50) | <(2; 3) + (3, 0, 0); 5 + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | Pban (50) | <(2; 3) + (5, 0, 0); 5 + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| Pban (50) | <3; 5; 2 + (0, 1, 0)> | a, 3b, c | | | Pban (50) | <3; 2 + (0, 3, 0); 5 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | Pban (50) | <3; 2 + (0, 5, 0); 5 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| Pban (50) | <2; 3; 5> | a, b, 3c | | | Pban (50) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | Pban (50) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| Pban (50) | <(2; 3) + (p/2 - 1/2 + 2u, 0, 0); 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
| Pban (50) | <3; 2 + (0, p/2 - 1/2 + 2u, 0); 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
| Pban (50) | <2; (3; 5) + (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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I Minimal translationengleiche supergroups
| [2] P4/nbm (125); [2] P42/nbc (133) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Cmmm (65); [2] Aeaa (68, Ccce); [2] Bbeb (68, Ccce); [2] Ibam (72) |
| [2] a' = 1/2a Pbmb (49, Pccm); [2] b' = 1/2b Pmaa (49, Pccm) |
