4/m 4/m Tetragonal No. 28 4/m Patterson symmetry 4/m

Origin at centre (4/m)

 Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1/2

Symmetry operations

 (1)  1 (2)  2   0, 0, z (3)  4+   0, 0, z (4)  4-   0, 0, z (5)  -1   0, 0, 0 (6)  m   x, y, 0 (7)  -4+   0, 0, z; 0, 0, 0 (8)  -4-   0, 0, z; 0, 0, 0

Generators selected (1); t(0, 0, 1); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 8 f 1
 (1) x, y, z (2) -x, -y, z (3) -y, x, z (4) y, -x, z (5) -x, -y, -z (6) x, y, -z (7) y, -x, -z (8) -y, x, -z
no conditions
Special: no extra conditions
 4 e m . .
 x, y, 1/2 -x, -y, 1/2 -y, x, 1/2 y, -x, 1/2
 4 d m . .
 x, y, 0 -x, -y, 0 -y, x, 0 y, -x, 0
 2 c 4 . .
 0, 0, z 0, 0, -z
 1 b 4/m . .
 0, 0, 1/2
 1 a 4/m . .
 0, 0, 0

Symmetry of special projections

 Along [001]   4Origin at 0, 0, z Along [100]   2mma' = c   Origin at x, 0, 0 Along [110]   2mma' = c   Origin at x, x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] -4 (27) 1; 2; 7; 8 [2] 4 (23) 1; 2; 3; 4 [2] 112/m (11) 1; 2; 5; 6
 IIa none
 IIb [2] 42/m (c' = 2c) (29)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 4/m (c' = 2c) (28)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] 4/mmm (39); [2] 4/mcc (40)
 II none