Origin at -4m 2, at 0, 1/4, -1/8 from centre (2/m)
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/8 |
For (0, 0, 0)+ set
| (1) 1 | (2) 2(0, 0, 1/2) 1/4, 1/4, z | (3) 4+(0, 0, 1/4) -1/4, 1/4, z | (4) 4-(0, 0, 3/4) 1/4, -1/4, z |
| (5) 2 1/4, y, 3/8 | (6) 2 x, 1/4, 1/8 | (7) 2(1/2, 1/2, 0) x, x, 1/4 | (8) 2 x, -x, 0 |
| (9) -1 0, 1/4, 1/8 | (10) a x, y, 3/8 | (11) -4+ 0, 0, z; 0, 0, 0 | (12) -4- 0, 1/2, z; 0, 1/2, 1/4 |
| (13) n(1/2, 0, 1/2) x, 1/4, z | (14) m 0, y, z | (15) d(1/4, -1/4, 3/4) x + 1/4, -x, z | (16) d(1/4, 1/4, 1/4) x - 1/4, x, z |
For (1/2, 1/2, 1/2)+ set
| (1) t(1/2, 1/2, 1/2) | (2) 2 0, 0, z | (3) 4+(0, 0, 3/4) 1/4, 1/4, z | (4) 4-(0, 0, 1/4) 1/4, 1/4, z |
| (5) 2(0, 1/2, 0) 0, y, 1/8 | (6) 2(1/2, 0, 0) x, 0, 3/8 | (7) 2 x, x, 0 | (8) 2 x, -x + 1/2, 1/4 |
| (9) -1 1/4, 0, 3/8 | (10) b x, y, 1/8 | (11) -4+ 1/2, 0, z; 1/2, 0, 1/4 | (12) -4- 0, 0, z; 0, 0, 0 |
| (13) m x, 0, z | (14) n(0, 1/2, 1/2) 1/4, y, z | (15) d(-1/4, 1/4, 1/4) x + 1/4, -x, z | (16) d(1/4, 1/4, 3/4) x + 1/4, x, z |
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); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ | General:
|
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z + 1/2 | (3) -y, x + 1/2, z + 1/4 | (4) y + 1/2, -x, z + 3/4 | | (5) -x + 1/2, y, -z + 3/4 | (6) x, -y + 1/2, -z + 1/4 | (7) y + 1/2, x + 1/2, -z + 1/2 | (8) -y, -x, -z | | (9) -x, -y + 1/2, -z + 1/4 | (10) x + 1/2, y, -z + 3/4 | (11) y, -x, -z | (12) -y + 1/2, x + 1/2, -z + 1/2 | | (13) x + 1/2, -y + 1/2, z + 1/2 | (14) -x, y, z | (15) -y + 1/2, -x, z + 3/4 | (16) y, x + 1/2, z + 1/4 |
| hkl : h + k + l = 2n
hk0 : h, k = 2n
0kl : k + l = 2n
hhl : 2h + l = 4n
00l : l = 4n
h00 : h = 2n
h-h0 : h = 2n
|
| | | Special: as above, plus
|
| | 0, y, z | 1/2, -y + 1/2, z + 1/2 | -y, 1/2, z + 1/4 | y + 1/2, 0, z + 3/4 | | 1/2, y, -z + 3/4 | 0, -y + 1/2, -z + 1/4 | y + 1/2, 1/2, -z + 1/2 | -y, 0, -z |
| no extra conditions |
| | x, x, 0 | -x + 1/2, -x + 1/2, 1/2 | -x, x + 1/2, 1/4 | x + 1/2, -x, 3/4 | | -x, -x + 1/2, 1/4 | x + 1/2, x, 3/4 | x, -x, 0 | -x + 1/2, x + 1/2, 1/2 |
| hkl : l = 2n + 1
or 2h + l = 4n
|
| | x, 1/4, 1/8 | -x + 1/2, 1/4, 5/8 | 3/4, x + 1/2, 3/8 | 3/4, -x, 7/8 | | -x, 1/4, 1/8 | x + 1/2, 1/4, 5/8 | 1/4, -x, 7/8 | 1/4, x + 1/2, 3/8 |
| hkl : l = 2n + 1
or h = 2n
|
| | 0, 0, z | 0, 1/2, z + 1/4 | 1/2, 0, -z + 3/4 | 1/2, 1/2, -z + 1/2 |
| hkl : l = 2n + 1
or 2h + l = 4n
|
| | 0, 1/4, 5/8 | 1/2, 1/4, 1/8 | 3/4, 1/2, 7/8 | 3/4, 0, 3/8 |
| hkl : l = 2n + 1 or h, k = 2n, h + k + l = 4n |
| | 0, 1/4, 1/8 | 1/2, 1/4, 5/8 | 3/4, 1/2, 3/8 | 3/4, 0, 7/8 |
|
| | hkl : l = 2n + 1 or 2h + l = 4n |
| |
Symmetry of special projections
Along [001] p4mm
a' = 1/2 a b' = 1/2b
Origin at 0, 0, z | Along [100] c2mm
a' = b b' = c
Origin at x, 0, 3/8 | Along [110] c2mm
a' = 1/2(-a + b) b' = 1/2c
Origin at x, x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] I-42d (122) | (1; 2; 5; 6; 11; 12; 15; 16)+ |
| | | [2] I-4m2 (119) | (1; 2; 7; 8; 11; 12; 13; 14)+ |
| | | [2] I41md (109) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
| | | [2] I4122 (98) | (1; 2; 3; 4; 5; 6; 7; 8)+ |
| | | [2] I41/a11 (I41/a, 88) | (1; 2; 3; 4; 9; 10; 11; 12)+ |
| | | [2] I2/a2/m1 (Imma, 74) | (1; 2; 5; 6; 9; 10; 13; 14)+ |
| | | [2] I2/a12/d (Fddd, 70) | (1; 2; 7; 8; 9; 10; 15; 16)+ |
Maximal isomorphic subgroups of lowest index
| IIc | [3] I41/amd (c' = 3c) (141); [9] I41/amd (a' = 3a, b' = 3b) (141) |
Minimal non-isomorphic supergroups
| II | [2] C42/amd (c' = 1/2c) (P42/nnm, 134) |
