[script p]42/m 4/m Tetragonal
No. 29 [script p]42/m Patterson symmetry [script p]4/m

symmetry group diagram

Origin at centre (2/m) on 42

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+ (1/2)   0, 0, z
      (4z | 0, 0, 1/2)
(4)  4- (1/2)   0, 0, z
      (4z-1 | 0, 0, 1/2)
(5)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(6)  m   xy, 0
      (mz | 0, 0, 0)
(7)  -4+   0, 0, z; 0, 0, 1/4
      (-4z | 0, 0, 1/2)
(8)  -4-   0, 0, z; 0, 0, 1/4
      (-4z-1 | 0, 0, 1/2)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
8 e 1
(1) xyz(2) -x-yz(3) -yxz + 1/2(4) y-xz + 1/2
(5) -x-y-z(6) xy-z(7) y-x-z + 1/2(8) -yx-z + 1/2
l: l = 2n
  Special: no extra conditions
4 d  m . . 
xy, 0-x-y, 0-yx1/2y-x1/2
4 c  2 . . 
0, 0, z0, 0, z + 1/20, 0, -z0, 0, -z + 1/2
2 b  -4 . . 
0, 0, 1/40, 0, 3/4
2 a  2/m . . 
0, 0, 00, 0, 1/2

Symmetry of special projections

Along [001]   4

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]-4 (27)1; 2; 7; 8
 [2] [script p]42 (25)1; 2; 3; 4
 [2] [script p]112/m (11)1; 2; 5; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]42/m (c' = 3c) (29)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]42/mmc (41)
II[2] [script p]4/m (c' = 1/2c) (28)








































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