Origin at centre (-3) at -3c
| Asymmetric unit | 1/4 ≤ x ≤ 5/4; 1/4 ≤ y ≤ 5/4; 1/4 ≤ z ≤ 3/4; y ≤ x; z ≤ min (y, 3/2 - x) |
| Vertices | | 1/4, 1/4, 1/4 | 5/4, 1/4, 1/4 | 5/4, 5/4, 1/4 | 3/4, 3/4, 3/4 |
|
| (1) 1 | (2) 3+ x, x, x | (3) 3- x, x, x |
| (4) 2 -x + 1/2, 1/4, x | (5) 2 x, -x + 1/2, 1/4 | (6) 2 1/4, y + 1/2, -y |
| (7) -1 0, 0, 0 | (8) -3+ x, x, x; 0, 0, 0 | (9) -3- x, x, x; 0, 0, 0 |
| (10) n(1/2, 1/2, 1/2) x, y, x | (11) n(1/2, 1/2, 1/2) x, x, z | (12) n(1/2, 1/2, 1/2) x, y, y |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4); (7)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) z, x, y | (3) y, z, x | | (4) -z + 1/2, -y + 1/2, -x + 1/2 | (5) -y + 1/2, -x + 1/2, -z + 1/2 | (6) -x + 1/2, -z + 1/2, -y + 1/2 | | (7) -x, -y, -z | (8) -z, -x, -y | (9) -y, -z, -x | | (10) z + 1/2, y + 1/2, x + 1/2 | (11) y + 1/2, x + 1/2, z + 1/2 | (12) x + 1/2, z + 1/2, y + 1/2 |
| hhl : l = 2n
hhh : h = 2n
|
| | | Special: as above, plus
|
| | x, -x + 1/2, 1/4 | 1/4, x, -x + 1/2 | -x + 1/2, 1/4, x | | -x, x + 1/2, 3/4 | 3/4, -x, x + 1/2 | x + 1/2, 3/4, -x |
| no extra conditions |
| | 1/2, 0, 0 | 0, 1/2, 0 | 0, 0, 1/2 | 1/2, 1/2, 0 | 1/2, 0, 1/2 | 0, 1/2, 1/2 |
| hkl : h + k + l = 2n
|
| | x, x, x | -x + 1/2, -x + 1/2, -x + 1/2 | -x, -x, -x | x + 1/2, x + 1/2, x + 1/2 |
| hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | 1/4, 1/4, 1/4 | 3/4, 3/4, 3/4 |
| hkl : h + k + l = 2n
|
Symmetry of special projections
Along [111] p6mm
a' = 1/3(2a - b - c) b' = 1/3(-a + 2b - c)
Origin at x, x, x | Along [1-10] p2
a' = 1/2(a + b - 2c) b' = 1/2c
Origin at x, -x, 0 | Along [2-1-1] p2gm
a' = 1/2(b - c) b' = 1/3(a + b + c)
Origin at 2x, -x, -x |
Maximal non-isomorphic subgroups
| I | | [2] R3c (161) | 1; 2; 3; 10; 11; 12 |
| | | [2] R32 (155) | 1; 2; 3; 4; 5; 6 |
| | | [2] R-31 (R-3, 148) | 1; 2; 3; 7; 8; 9 |
| | ![[brace]](/graphics/sg/brace3.gif) | [3] R12/c (C2/c, 15) | 1; 4; 7; 10 | | | [3] R12/c (C2/c, 15) | 1; 5; 7; 11 | | | [3] R12/c (C2/c, 15) | 1; 6; 7; 12 |
|
| IIb | [3] P-3c1 (a' = a - b, b' = b - c, c' = a + b + c) (165) |
Maximal isomorphic subgroups of lowest index
| IIc | [4] R-3c (a' = -a + b + c, b' = a - b + c, c' = a + b - c) (167); [5] R-3c (a' = a + 2b + 2c, b' = 2a + b + 2c, c' = 2a + 2b + c) (167) |
Minimal non-isomorphic supergroups
| I | [4] Pn-3n (222); [4] Pm-3n (223); [4] Fm-3c (226); [4] Fd-3c (228); [4] Ia-3d (230) |
| II | [2] R-3m (a' = 1/2(-a + b + c), b' = 1/2(a - b + c), c' = 1/2(a + b - c)) (166); [3] P-31c (a' = 1/3(2a - b - c), b' = 1/3(-a + 2b - c), c' = 1/3(a + b + c)) (163) |
