[script p]4322 422 Tetragonal
No. 33 [script p]4322 Patterson symmetry [script p]4/mmm

symmetry group diagram

Origin on 2[100] at 43(2,1)1

Asymmetric unit 0 ≤ z ≤ 1/8

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2 (1/2)   0, 0, z
      (2z | 0, 0, 1/2)
(3)  4+ (3/4)   0, 0, z
      (4z | 0, 0, 3/4)
(4)  4- (1/4)   0, 0, z
      (4z-1 | 0, 0, 1/4)
(5)  2   x, 0, 0
      (2x | 0, 0, 0)
(6)  2   0, y1/4
      (2y | 0, 0, 1/2)
(7)  2   xx3/8
      (2xy | 0, 0, 3/4)
(8)  2   x-x1/8
      (2-xy | 0, 0, 1/4)

Generators selected (1); t(0, 0, 1); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
8 c 1
(1) xyz(2) -x-yz + 1/2(3) -yxz + 3/4(4) y-xz + 1/4
(5) x-y-z(6) -xy-z + 1/2(7) yx-z + 3/4(8) -y-x-z + 1/4
l: l = 4n
  Special: no extra conditions
4 b  . . 2 
xx7/8-x-x3/8-xx5/8x-x1/8
4 a  . 2 . 
x, 0, 0-x, 0, 1/20, x3/40, -x1/4

Symmetry of special projections

Along [001]   4mm

Origin at 0, 0, z
Along [100]   [script p]2mg
a' = c   
Origin at x, 0, 0
Along [110]   [script p]2mg
a' = c   
Origin at xx3/8

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]4311 ([script p]43, 26)1; 2; 3; 4
 [2] [script p]2121 ([script p]2221, 14)1; 2; 5; 6
 [2] [script p]2112 ([script p]2221, 14)1; 2; 7; 8
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]4122 (c' = 3c) (31); [5] [script p]4322 (c' = 5c) (33)

Minimal non-isotypic non-enantiomorphic supergroups


Inone
II[2] [script p]4222 (c' = 1/2c) (32)








































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