[script p]31c 31m Trigonal
No. 50 [script p]31c Patterson symmetry [script p]-31m
SECOND SETTING

symmetry group diagram

Origin on 31c

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1/2

Symmetry operations

(1)  1   (2)  3+   0, 0, z(3)  3-   0, 0, z
(4)  c   x, x, z(5)  c   x, 0, z(6)  c   0, y, z

Generators selected (1); t(0, 0, 1); (2); (4)

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
6 b 1
(1) x, y, z(2) -y, x - y, z(3) -x + y, -x, z
(4) y, x, z + 1/2(5) x - y, -y, z + 1/2(6) -x, -x + y, z + 1/2
l: l = 2n
  Special: no extra conditions
2 a  3 . . 
0, 0, z0, 0, z + 1/2

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z 		Along [100]   [script p]11g
a' = c   
Origin at x, 0, 0 		Along [210]   [script p]1
a' = 1/2c   
Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

I[2] [script p]311 ([script p]3, 42)1; 2; 3
 [3] [script p]11c ([script p]c11, 5)1; 4
 [3] [script p]11c ([script p]c11, 5)1; 5
 [3] [script p]11c ([script p]c11, 5)1; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

IIc[3] [script p]31c (c' = 3c) ([script p]3c1, 50)

Minimal non-isotypic non-enantiomorphic supergroups

I[2] [script p]-31c (52); [2] [script p]6cc (69); [2] [script p]63mc (70); [2] [script p]-6c2 (72)
II[2] [script p]3m1 (c' = 1/2c) (49)








































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