[script p]3112 312 Trigonal
No. 47 [script p]3112 Patterson symmetry [script p]-31m
FIRST SETTING

symmetry group diagram

Origin on 2[210] at 311(1,1,2)

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

Symmetry operations

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

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

Positions

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

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z 		Along [100]   [script p]1m1
a' = c   
Origin at x, 0, 1/6 		Along [210]   [script p]211
a' = c   
Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

I[2] [script p]3111 ([script p]31, 43)1; 2; 3
 [3] [script p]112 ([script p]211, 3)1; 4
 [3] [script p]112 ([script p]211, 3)1; 5
 [3] [script p]112 ([script p]211, 3)1; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

IIc[2] [script p]3212 (c' = 2c) (48); [7] [script p]3112 (c' = 7c) (47)

Minimal non-isotypic non-enantiomorphic supergroups

I[2] [script p]6122 (63); [2] [script p]6422 (66)
II[3] [script p]312 (c' = 1/3c) (46)








































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