p-4 -4 Tetragonal/Square No. 50 p-4 Patterson symmetry p4/m

Origin at -4

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

Symmetry operations

 (1)  1       (1 | 0, 0, 0) (2)  2   0, 0, z       (2z | 0, 0, 0) (3)  -4+   0, 0, z; 0, 0, 0       (-4z | 0, 0, 0) (4)  -4-   0, 0, z; 0, 0, 0       (-4z-1 | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 f 1
 (1) x, y, z (2) -x, -y, z (3) y, -x, -z (4) -y, x, -z
no conditions
Special:
 2 e 2 . .
 0, 1/2, z 1/2, 0, -z
hk: h + k = 2n
 2 d 2 . .
 1/2, 1/2, z 1/2, 1/2, -z
no extra conditions
 2 c 2 . .
 0, 0, z 0, 0, -z
no extra conditions
 1 b -4 . .
 1/2, 1/2, 0
no extra conditions
 1 a -4 . .
 0, 0, 0
no extra conditions

Symmetry of special projections

 Along [001]   p4 a' = a   b' = b    Origin at 0, 0, z Along [100]   1m1 a' = b    Origin at x, 0, 0 Along [110]   1m1 a' = 1/2(-a + b)    Origin at x, x, 0

Maximal non-isotypic subgroups

 I [2] p211 (p112, 3) 1; 2
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [2] c-4 (a' = 2a, b' = 2b) (p-4, 50)

Minimal non-isotypic supergroups

 I [2] p4/m (51); [2] p4/n (52); [2] p-42m (57); [2] p-421m (58); [2] p-4m2 (59); [2] p-4b2 (60)
 II none