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    (2)  2   0, 0, z (3)  -4+   0, 0, z; 0, 0, 0 (4)  -4-   0, 0, z; 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]   [script p]1m1
a' = b   
Origin at x, 0, 0		 Along [110]   [script p]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








































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