[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   (2)  2   0, 0, z(3)  4+   0, 0, z(4)  4-   0, 0, z
(5)  2   0, y, 0(6)  2   x, 0, 0(7)  2   x, x, 0(8)  2   x, -x, 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) x, y, z(2) -x, -y, z(3) -y, x, z(4) y, -x, z
(5) -x, y, -z(6) x, -y, -z(7) y, x, -z(8) -y, -x, -z
no conditions
  Special: no extra conditions
4 g  . 2 . 
x, 0, 1/2-x, 0, 1/20, x, 1/20, -x, 1/2
4 f  . 2 . 
x, 0, 0-x, 0, 00, x, 00, -x, 0
4 e  . . 2 
x, x, 1/2-x, -x, 1/2-x, x, 1/2x, -x, 1/2
4 d  . . 2 
x, x, 0-x, -x, 0-x, x, 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 x, x, 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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