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); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x + 1/2, -y, z + 1/2 | (3) -x, y + 1/2, -z + 1/2 | (4) x + 1/2, -y + 1/2, -z | | (5) z, x, y | (6) z + 1/2, -x + 1/2, -y | (7) -z + 1/2, -x, y + 1/2 | (8) -z, x + 1/2, -y + 1/2 | | (9) y, z, x | (10) -y, z + 1/2, -x + 1/2 | (11) y + 1/2, -z + 1/2, -x | (12) -y + 1/2, -z, x + 1/2 | | (13) y + 3/4, x + 1/4, -z + 1/4 | (14) -y + 3/4, -x + 3/4, -z + 3/4 | (15) y + 1/4, -x + 1/4, z + 3/4 | (16) -y + 1/4, x + 3/4, z + 1/4 | | (17) x + 3/4, z + 1/4, -y + 1/4 | (18) -x + 1/4, z + 3/4, y + 1/4 | (19) -x + 3/4, -z + 3/4, -y + 3/4 | (20) x + 1/4, -z + 1/4, y + 3/4 | | (21) z + 3/4, y + 1/4, -x + 1/4 | (22) z + 1/4, -y + 1/4, x + 3/4 | (23) -z + 1/4, y + 3/4, x + 1/4 | (24) -z + 3/4, -y + 3/4, -x + 3/4 |
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I Maximal translationengleiche subgroups
| [2] I2131 (199, I213) | (1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12)+ |
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 | [3] I4112 (98, I4122) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
| 0, 1/4, 1/8
| | [3] I4112 (98, I4122) | (1; 4; 2; 3; 18; 19; 17; 20)+ | b, c, a
| 1/8, 0, 1/4
| | [3] I4112 (98, I4122) | (1; 3; 4; 2; 22; 24; 23; 21)+ | c, a, b
| 1/4, 1/8, 0
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 | [4] I132 (155, R32) | (1; 5; 9; 14; 19; 24)+ | -a + b, -b + c, 1/2(a + b + c)
| 1/8, 1/8, 1/8
| | [4] I132 (155, R32) | (1; 6; 12; 13; 18; 24)+ | a + b, -b - c, 1/2(-a + b - c)
| 7/8, 5/8, 3/8
| | [4] I132 (155, R32) | (1; 7; 10; 13; 19; 22)+ | -a - b, b - c, 1/2(a - b - c)
| 5/8, 3/8, 7/8
| | [4] I132 (155, R32) | (1; 8; 11; 14; 18; 22)+ | a - b, b + c, 1/2(-a - b + c)
| 3/8, 7/8, 5/8
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P4132 (213) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24 | | |
| [2] P4332 (212) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; (13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24) + (1/2, 1/2, 1/2) | | |
- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| I4132 (214) | <2 + (p/2 - 1/2 + 2u, 2v, p/2 - 1/2); 3 + (2u, p/2 - 1/2, p/2 - 1/2 + 2w); 5 + (u - w, -u + v, -v + w); 13 + (3p/4 - 3/4 + u - v, p/4 - 1/4 - u + v, p/4 - 1/4 + 2w)> | pa, pb, pc | u, v, w | | | p > 2; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [4] a' = 1/2a, b' = 1/2b, c' = 1/2c P4232 (208) |
