ORIGIN CHOICE 1, Origin at 2 3, at -1/8, -1/8, -1/8 from centre (-3)
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); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (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) z, x, y | (6) z, -x, -y | (7) -z, -x, y | (8) -z, x, -y | | (9) y, z, x | (10) -y, z, -x | (11) y, -z, -x | (12) -y, -z, x | | (13) -x + 1/4, -y + 1/4, -z + 1/4 | (14) x + 1/4, y + 1/4, -z + 1/4 | (15) x + 1/4, -y + 1/4, z + 1/4 | (16) -x + 1/4, y + 1/4, z + 1/4 | | (17) -z + 1/4, -x + 1/4, -y + 1/4 | (18) -z + 1/4, x + 1/4, y + 1/4 | (19) z + 1/4, x + 1/4, -y + 1/4 | (20) z + 1/4, -x + 1/4, y + 1/4 | | (21) -y + 1/4, -z + 1/4, -x + 1/4 | (22) y + 1/4, -z + 1/4, x + 1/4 | (23) -y + 1/4, z + 1/4, x + 1/4 | (24) y + 1/4, z + 1/4, -x + 1/4 |
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I Maximal translationengleiche subgroups
| [2] F23 (196) | (1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12)+ |
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| [3] Fd1 (70, Fddd) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
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 | [4] F1-3 (148, R-3) | (1; 5; 9; 13; 17; 21)+ | 1/2(-a + b), 1/2(-b + c), a + b + c
| 1/8, 1/8, 1/8
| | [4] F1-3 (148, R-3) | (1; 6; 12; 13; 18; 24)+ | 1/2(a + b), 1/2(-b - c), -a + b - c
| 3/8, 1/8, 3/8
| | [4] F1-3 (148, R-3) | (1; 7; 10; 13; 19; 22)+ | 1/2(-a - b), 1/2(b - c), a - b - c
| 1/8, 3/8, 3/8
| | [4] F1-3 (148, R-3) | (1; 8; 11; 13; 20; 23)+ | 1/2(a - b), 1/2(b + c), -a - b + c
| 3/8, 3/8, 1/8
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II Maximal klassengleiche subgroups
- Loss of centring translations
- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| Fd-3 (203) | <2 + (1/2 + 2u, 1/2 + 2v, 0); 3 + (1/2 + 2u, 0, 1/2 + 2w); 5 + (u - w, -u + v, -v + w); 13 + (p/4 + 1/4 + 2u, p/4 + 1/4 + 2v, p/4 + 1/4 + 2w)> | pa, pb, pc | 1/4 + u, 1/4 + v, 1/4 + w | | | p > 2; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for prime p ≡ 3 (mod 4) |
| Fd-3 (203) | <2 + (2u, 2v, 0); 3 + (2u, 0, 2w); 5 + (u - w, -u + v, -v + w); 13 + (p/4 - 1/4 + 2u, p/4 - 1/4 + 2v, 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 prime p ≡ 1 (mod 4) |
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I Minimal translationengleiche supergroups
| [2] Fd-3m (227); [2] Fd-3c (228) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] a' = 1/2a, b' = 1/2b, c' = 1/2c Pn-3 (201) |
