ORIGIN CHOICE 1, Origin at 2 3, at -1/4, -1/4, -1/4 from centre (-3)
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (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 + 1/2, -y + 1/2, -z + 1/2 | (14) x + 1/2, y + 1/2, -z + 1/2 | (15) x + 1/2, -y + 1/2, z + 1/2 | (16) -x + 1/2, y + 1/2, z + 1/2 | | (17) -z + 1/2, -x + 1/2, -y + 1/2 | (18) -z + 1/2, x + 1/2, y + 1/2 | (19) z + 1/2, x + 1/2, -y + 1/2 | (20) z + 1/2, -x + 1/2, y + 1/2 | | (21) -y + 1/2, -z + 1/2, -x + 1/2 | (22) y + 1/2, -z + 1/2, x + 1/2 | (23) -y + 1/2, z + 1/2, x + 1/2 | (24) y + 1/2, z + 1/2, -x + 1/2 |
|
I Maximal translationengleiche subgroups
| [2] P23 (195) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12 |
|
|
| [3] Pn1 (48, Pnnn) | 1; 2; 3; 4; 13; 14; 15; 16 |
|
|
 | [4] P1-3 (148, R-3) | 1; 5; 9; 13; 17; 21 | a - b, b - c, a + b + c
| 1/4, 1/4, 1/4
| | [4] P1-3 (148, R-3) | 1; 6; 12; 13; 18; 24 | -a - b, b + c, -a + b - c
| 3/4, 1/4, 3/4
| | [4] P1-3 (148, R-3) | 1; 7; 10; 13; 19; 22 | a + b, -b + c, a - b - c
| 1/4, 3/4, 3/4
| | [4] P1-3 (148, R-3) | 1; 8; 11; 13; 20; 23 | -a + b, -b - c, -a - b + c
| 3/4, 3/4, 1/4
|
|
II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| Fd-3 (203) | <2; 3; 5; 13> | 2a, 2b, 2c | |
| Fd-3 (203) | <2; 3; 5; 13 + (1, 1, 1)> | 2a, 2b, 2c | 1/2, 1/2, 1/2 |
- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| Pn-3 (201) | <2 + (2u, 2v, 0); 3 + (2u, 0, 2v); 5 + (u - w, -u + v, -v + w); 13 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, p/2 - 1/2 + 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 |
|
I Minimal translationengleiche supergroups
| [2] Pn-3n (222); [2] Pn-3m (224) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Im-3 (204); [4] Fm-3 (202) |
ORIGIN CHOICE 2, Origin at centre -3, at 1/4, 1/4, 1/4 from 2 3
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (13)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
|
| | |
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z | (3) -x + 1/2, y, -z + 1/2 | (4) x, -y + 1/2, -z + 1/2 | | (5) z, x, y | (6) z, -x + 1/2, -y + 1/2 | (7) -z + 1/2, -x + 1/2, y | (8) -z + 1/2, x, -y + 1/2 | | (9) y, z, x | (10) -y + 1/2, z, -x + 1/2 | (11) y, -z + 1/2, -x + 1/2 | (12) -y + 1/2, -z + 1/2, x | | (13) -x, -y, -z | (14) x + 1/2, y + 1/2, -z | (15) x + 1/2, -y, z + 1/2 | (16) -x, y + 1/2, z + 1/2 | | (17) -z, -x, -y | (18) -z, x + 1/2, y + 1/2 | (19) z + 1/2, x + 1/2, -y | (20) z + 1/2, -x, y + 1/2 | | (21) -y, -z, -x | (22) y + 1/2, -z, x + 1/2 | (23) -y, z + 1/2, x + 1/2 | (24) y + 1/2, z + 1/2, -x |
|
I Maximal translationengleiche subgroups
| [2] P23 (195) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12 |
| 1/4, 1/4, 1/4
|
| [3] Pn1 (48, Pnnn) | 1; 2; 3; 4; 13; 14; 15; 16 |
|
|
| [4] P1-3 (148, R-3) | 1; 5; 9; 13; 17; 21 | a - b, b - c, a + b + c
|
| | [4] P1-3 (148, R-3) | 1; 6; 12; 13; 18; 24 | -a - b, b + c, -a + b - c
| 1/2, 0, 1/2
| | [4] P1-3 (148, R-3) | 1; 7; 10; 13; 19; 22 | a + b, -b + c, a - b - c
| 0, 1/2, 1/2
| | [4] P1-3 (148, R-3) | 1; 8; 11; 13; 20; 23 | -a + b, -b - c, -a - b + c
| 1/2, 1/2, 0
|
|
II Maximal klassengleiche subgroups
[2] a' = 2a, b' = 2b, c' = 2c
| Fd-3 (203) | <2; 3; 5; 13> | 2a, 2b, 2c | |
| Fd-3 (203) | <2; 3; 5; 13 + (1, 1, 1)> | 2a, 2b, 2c | 1/2, 1/2, 1/2 |
- Series of maximal isomorphic subgroups
[p3] a' = pa, b' = pb, c' = pc
| Pn-3 (201) | <2 + (p/2 - 1/2 + 2u, p/2 - 1/2 + 2v, 0); 3 + (p/2 - 1/2 + 2u, 0, p/2 - 1/2 + 2w); 5 + (u - w, -u + v, -v + w); 13 + (2u, 2v, 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 |
|
I Minimal translationengleiche supergroups
| [2] Pn-3n (222); [2] Pn-3m (224) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] Im-3 (204); [4] Fm-3 (202) |
