Origin at centre (4/m) at 4/m 1 n
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/4 |
| (1) 1 | (2) 2 0, 0, z | (3) 4+ 0, 0, z | (4) 4- 0, 0, z |
| (5) 2(0, 1/2, 0) 1/4, y, 1/4 | (6) 2(1/2, 0, 0) x, 1/4, 1/4 | (7) 2(1/2, 1/2, 0) x, x, 1/4 | (8) 2 x, -x + 1/2, 1/4 |
| (9) -1 0, 0, 0 | (10) m x, y, 0 | (11) -4+ 0, 0, z; 0, 0, 0 | (12) -4- 0, 0, z; 0, 0, 0 |
| (13) n(1/2, 0, 1/2) x, 1/4, z | (14) n(0, 1/2, 1/2) 1/4, y, z | (15) c x + 1/2, -x, z | (16) n(1/2, 1/2, 1/2) x, x, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -x, -y, z | (3) -y, x, z | (4) y, -x, z | | (5) -x + 1/2, y + 1/2, -z + 1/2 | (6) x + 1/2, -y + 1/2, -z + 1/2 | (7) y + 1/2, x + 1/2, -z + 1/2 | (8) -y + 1/2, -x + 1/2, -z + 1/2 | | (9) -x, -y, -z | (10) x, y, -z | (11) y, -x, -z | (12) -y, x, -z | | (13) x + 1/2, -y + 1/2, z + 1/2 | (14) -x + 1/2, y + 1/2, z + 1/2 | (15) -y + 1/2, -x + 1/2, z + 1/2 | (16) y + 1/2, x + 1/2, z + 1/2 |
| 0kl : k + l = 2n
hhl : l = 2n
00l : l = 2n
h00 : h = 2n
|
| | | Special: as above, plus
|
| | x, y, 0 | -x, -y, 0 | -y, x, 0 | y, -x, 0 | | -x + 1/2, y + 1/2, 1/2 | x + 1/2, -y + 1/2, 1/2 | y + 1/2, x + 1/2, 1/2 | -y + 1/2, -x + 1/2, 1/2 |
| no extra conditions |
| | x, x + 1/2, 1/4 | -x, -x + 1/2, 1/4 | -x + 1/2, x, 1/4 | x + 1/2, -x, 1/4 | | -x, -x + 1/2, 3/4 | x, x + 1/2, 3/4 | x + 1/2, -x, 3/4 | -x + 1/2, x, 3/4 |
| hkl : l = 2n
|
| | 0, 1/2, z | 1/2, 0, z | 1/2, 0, -z + 1/2 | 0, 1/2, -z + 1/2 | | 0, 1/2, -z | 1/2, 0, -z | 1/2, 0, z + 1/2 | 0, 1/2, z + 1/2 |
| hkl : h + k, l = 2n
|
| | 0, 0, z | 1/2, 1/2, -z + 1/2 | 0, 0, -z | 1/2, 1/2, z + 1/2 |
| hkl : h + k + l = 2n
|
| | 0, 1/2, 1/4 | 1/2, 0, 1/4 | 0, 1/2, 3/4 | 1/2, 0, 3/4 |
| hkl : h + k, l = 2n
|
| | 0, 1/2, 0 | 1/2, 0, 0 | 1/2, 0, 1/2 | 0, 1/2, 1/2 |
| hkl : h + k, l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
Symmetry of special projections
Along [001] p4gm
a' = a b' = b
Origin at 0, 0, z | Along [100] c2mm
a' = b b' = c
Origin at x, 0, 0 | Along [110] p2mm
a' = 1/2(-a + b) b' = 1/2c
Origin at x, x, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P-4n2 (118) | 1; 2; 7; 8; 11; 12; 13; 14 |
| | | [2] P-421c (114) | 1; 2; 5; 6; 11; 12; 15; 16 |
| | | [2] P4nc (104) | 1; 2; 3; 4; 13; 14; 15; 16 |
| | | [2] P4212 (90) | 1; 2; 3; 4; 5; 6; 7; 8 |
| | | [2] P4/m11 (P4/m, 83) | 1; 2; 3; 4; 9; 10; 11; 12 |
| | | [2] P2/m12/c (Cccm, 66) | 1; 2; 7; 8; 9; 10; 15; 16 |
| | | [2] P2/m21/n1 (Pnnm, 58) | 1; 2; 5; 6; 9; 10; 13; 14 |
Maximal isomorphic subgroups of lowest index
| IIc | [3] P4/mnc (c' = 3c) (128); [9] P4/mnc (a' = 3a, b' = 3b) (128) |
Minimal non-isomorphic supergroups
| II | [2] C4/mcc (P4/mcc, 124); [2] I4/mmm (139); [2] P4/mbm (c' = 1/2c) (127) |
