[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   (2)  2   0, 0, z(3)  4+(1/2)   0, 0, z(4)  4-(1/2)   0, 0, z
(5)  -1   0, 0, 0(6)  m   x, y, 0(7)  -4+   0, 0, z; 0, 0, 1/4(8)  -4-   0, 0, z; 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 e 1
(1) x, y, z(2) -x, -y, z(3) -y, x, z + 1/2(4) y, -x, z + 1/2
(5) -x, -y, -z(6) x, y, -z(7) y, -x, -z + 1/2(8) -y, x, -z + 1/2
l: l = 2n
  Special: no extra conditions
4 d  m . . 
x, y, 0-x, -y, 0-y, x, 1/2y, -x, 1/2
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 x, x, 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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