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

symmetry group diagram

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) xyz (2) -x-yz (3) y-x-z (4) -yx-z
no conditions
    Special:
2 e  2 . . 
0, 1/2z 1/2, 0, -z
hk: h + k = 2n
2 d  2 . . 
1/21/2z 1/21/2-z
no extra conditions
2 c  2 . . 
0, 0, z 0, 0, -z
no extra conditions
1 b  -4 . . 
1/21/2, 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]   [script p]1m1
a' = b   
Origin at x, 0, 0
Along [110]   [script p]1m1
a' = 1/2(-a + b)   
Origin at xx, 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' = 2ab' = 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








































to end of page
to top of page