[script p]6 6 Hexagonal
No. 53 [script p]6 Patterson symmetry [script p]6/m

symmetry group diagram

Origin on 6

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

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

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

Symmetry of special projections

Along [001]   6

Origin at 0, 0, z
Along [100]   [script p]11m
a' = c   
Origin at x, 0, 0
Along [210]   [script p]11m
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]112 (8)1; 4
IIa none
IIb[2] [script p]63 (c' = 2c) (56); [3] [script p]64 (c' = 3c) (57); [3] [script p]62 (c' = 3c) (55)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]6 (c' = 2c) (53)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6/m (60); [2] [script p]622 (62); [2] [script p]6mm (68); [2] [script p]6cc (69)
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