p4 4 Tetragonal/Square
No. 49 p4 Patterson symmetry p4/m

symmetry group diagram

Origin on 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
      (4z | 0, 0, 0)
(4)  4-   0, 0, z
      (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 d 1
(1) xyz (2) -x-yz (3) -yxz (4) y-xz
no conditions
    Special:
2 c  2 . . 
0, 1/2z 1/2, 0, z
hk: h + k = 2n
1 b  4 . . 
1/21/2z
no extra conditions
1 a  4 . . 
0, 0, z
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] c4 (a' = 2ab' = 2b) (p4, 49)

Minimal non-isotypic supergroups


I [2] p4/m (51); [2] p4/n (52); [2] p422 (53); [2] p4212 (54); [2] p4mm (55); [2] p4bm (56)
II none








































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