p4/m 4/m Tetragonal/Square
No. 51 p4/m Patterson symmetry p4/m

symmetry group diagram

Origin at centre (4/m)

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

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)
(5)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(6)  m   xy, 0
      (mz | 0, 0, 0)
(7)  -4+   0, 0, z; 0, 0, 0
      (-4z | 0, 0, 0)
(8)  -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); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  General:
8 h 1
(1) xyz (2) -x-yz (3) -yxz (4) y-xz
(5) -x-y-z (6) xy-z (7) y-x-z (8) -yx-z
no conditions
    Special:
4 g  m . . 
xy, 0 -x-y, 0 -yx, 0 y-x, 0
no extra conditions
4 f  2 . . 
0, 1/2z 1/2, 0, z 0, 1/2-z 1/2, 0, -z
hk: h + k = 2n
2 e  4 . . 
1/21/2z 1/21/2-z
no extra conditions
2 d  4 . . 
0, 0, z 0, 0, -z
no extra conditions
2 c  2/m . . 
0, 1/2, 0 1/2, 0, 0
hk: h + k = 2n
1 b  4/m . . 
1/21/2, 0
no extra conditions
1 a  4/m . . 
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]2mm
a' = b   
Origin at x, 0, 0
Along [110]   [script p]2mm
a' = 1/2(-a + b)   
Origin at xx, 0

Maximal non-isotypic subgroups


I [2] p-4 (50) 1; 2; 7; 8
  [2] p4 (49) 1; 2; 3; 4
  [2] p2/m11 (p112/m, 6) 1; 2; 5; 6
IIa none
IIb [2] c4/a (a' = 2ab' = 2b) (p4/n, 52)

Maximal isotypic subgroups of lowest index


IIc [2] c4/m (a' = 2ab' = 2b) (p4/m, 51)

Minimal non-isotypic supergroups


I [2] p4/mmm (61); [2] p4/mbm (63)
II none








































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