[script p]-42m -42m Tetragonal
No. 37 [script p]-42m Patterson symmetry [script p]4/mmm
FIRST SETTING

symmetry group diagram

Origin at -42m

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

Symmetry operations

(1)  1   (2)  2   0, 0, z(3)  -4+   0, 0, z; 0, 0, 0(4)  -4-   0, 0, z; 0, 0, 0
(5)  2   0, y, 0(6)  2   x, 0, 0(7)  m   x, -x, z(8)  m   x, x, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
8 g 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 f  . . m 
x, x, z-x, -x, zx, -x, -z-x, x, -z
4 e  . 2 . 
x, 0, 1/2-x, 0, 1/20, -x, 1/20, x, 1/2
4 d  . 2 . 
x, 0, 0-x, 0, 00, -x, 00, x, 0
2 c  2 . mm 
0, 0, z0, 0, -z
1 b  -4 2 m 
0, 0, 1/2
1 a  -4 2 m 
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]11m
a' = c   
Origin at x, x, 0

Maximal non-isotypic non-enantiomorphic subgroups

I[2] [script p]-411 ([script p]-4, 27)1; 2; 3; 4
 [2] [script p]21m ([script p]mm2, 15)1; 2; 7; 8
 [2] [script p]221 ([script p]222, 13)1; 2; 5; 6
IIa none
IIb[2] [script p]-42c (c' = 2c) (38)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

IIc[2] [script p]-42m (c' = 2c) (37)

Minimal non-isotypic non-enantiomorphic supergroups

I[2] [script p]4/mmm (39); [2] [script p]42/mmc (41)
IInone








































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