[script p]-3 -3 Trigonal
No. 45 [script p]-3 Patterson symmetry [script p]-3

symmetry group diagram

Origin at centre (-3)

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  3+   0, 0, z
      (3z | 0, 0, 0)
(3)  3-   0, 0, z
      (3z-1 | 0, 0, 0)
(4)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(5)  -3+   0, 0, z; 0, 0, 0
      (-3z | 0, 0, 0)
(6)  -3-   0, 0, z; 0, 0, 0
      (-3z-1 | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
6 d 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) -x-y-z(5) y-x + y-z(6) x - yx-z
no conditions
  Special: no extra conditions
2 c  3 . . 
0, 0, z0, 0, -z
1 b  -3 . . 
0, 0, 1/2
1 a  -3 . . 
0, 0, 0

Symmetry of special projections

Along [001]   6

Origin at 0, 0, z
Along [100]   [script p]211
a' = c   
Origin at x, 0, 0
Along [210]   [script p]211
a' = c   
Origin at x1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]3 (42)1; 2; 3
 [3] [script p]-1 (2)1; 4
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]-3 (c' = 2c) (45)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]-31m (51); [2] [script p]-31c (52); [2] [script p]6/m (60); [2] [script p]63/m (61)
IInone








































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