[script p]422 422 Tetragonal
No. 30 [script p]422 Patterson symmetry [script p]4/mmm

symmetry group diagram

Origin at 422

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 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)
(5)  2   0, y, 0
      (2y | 0, 0, 0)
(6)  2   x, 0, 0
      (2x | 0, 0, 0)
(7)  2   xx, 0
      (2xy | 0, 0, 0)
(8)  2   x-x, 0
      (2-xy | 0, 0, 0)

Generators selected (1); t(0, 0, 1); (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) -xy-z(6) x-y-z(7) yx-z(8) -y-x-z
no conditions
  Special: no extra conditions
4 g  . 2 . 
x, 0, 1/2-x, 0, 1/20, x1/20, -x1/2
4 f  . 2 . 
x, 0, 0-x, 0, 00, x, 00, -x, 0
4 e  . . 2 
xx1/2-x-x1/2-xx1/2x-x1/2
4 d  . . 2 
xx, 0-x-x, 0-xx, 0x-x, 0
2 c  4 . . 
0, 0, z0, 0, -z
1 b  4 2 2 
0, 0, 1/2
1 a  4 2 2 
0, 0, 0

Symmetry of special projections

Along [001]   4mm

Origin at 0, 0, z
Along [100]   [script p]2mm
a' = c   
Origin at x, 0, 0
Along [110]   [script p]2mm
a' = c   
Origin at xx, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]411 ([script p]4, 23)1; 2; 3; 4
 [2] [script p]221 ([script p]222, 13)1; 2; 5; 6
 [2] [script p]212 ([script p]222, 13)1; 2; 7; 8
IIa none
IIb[2] [script p]4222 (c' = 2c) (32)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]422 (c' = 2c) (30)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]4/mmm (39); [2] [script p]4/mcc (40)
IInone








































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