[script p]4122 422 Tetragonal
No. 31 [script p]4122 Patterson symmetry [script p]4/mmm

symmetry group diagram

Origin on 2[100] at 41(2,1)1

Asymmetric unit 0 ≤ z ≤ 1/8

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
8 c 1
(1) x, y, z(2) -x, -y, z + 1/2(3) -y, x, z + 1/4(4) y, -x, z + 3/4
(5) x, -y, -z(6) -x, y, -z + 1/2(7) y, x, -z + 1/4(8) -y, -x, -z + 3/4
l: l = 4n
  Special: no extra conditions
4 b  . . 2 
x, x, 1/8-x, -x, 5/8-x, x, 3/8x, -x, 7/8
4 a  . 2 . 
x, 0, 0-x, 0, 1/20, x, 1/40, -x, 3/4

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 x, x, 1/8

Maximal non-isotypic non-enantiomorphic subgroups

I[2] [script p]4111 ([script p]41, 24)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]4322 (c' = 3c) (33); [5] [script p]4122 (c' = 5c) (31)

Minimal non-isotypic non-enantiomorphic supergroups

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








































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