[script p]42 4 Tetragonal
No. 25 [script p]42 Patterson symmetry [script p]4/m

symmetry group diagram

Origin on 2 on 42

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  4+ (1/2)   0, 0, z
      (4z | 0, 0, 1/2)
(4)  4- (1/2)   0, 0, z
      (4z-1 | 0, 0, 1/2)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
4 b 1
(1) xyz(2) -x-yz(3) -yxz + 1/2(4) y-xz + 1/2
l: l = 2n
  Special: no extra conditions
2 a  2 . . 
0, 0, z0, 0, z + 1/2

Symmetry of special projections

Along [001]   4

Origin at 0, 0, z
Along [100]   [script p]11m
a' = c   
Origin at x, 0, 0
Along [110]   [script p]11m
a' = c   
Origin at xx, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]112 (8)1; 2
IIa none
IIb[2] [script p]43 (c' = 2c) (26); [2] [script p]41 (c' = 2c) (24)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]42 (c' = 3c) (25)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]42/m (29); [2] [script p]4222 (32); [2] [script p]42cm (35)
II[2] [script p]4 (c' = 1/2c) (23)








































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