[script p]63 6 Hexagonal
No. 56 [script p]63 Patterson symmetry [script p]6/m

symmetry group diagram

Origin on 3 on 63

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

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 + 1/2(5) y-x + yz + 1/2(6) x - yxz + 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]   6

Origin at 0, 0, z
Along [100]   [script p]11g
a' = c   
Origin at x, 0, 0
Along [210]   [script p]11g
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]1121 (9)1; 4
IIa none
IIb[3] [script p]65 (c' = 3c) (58); [3] [script p]61 (c' = 3c) (54)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]63 (c' = 3c) (56)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]63/m (61); [2] [script p]6322 (65); [2] [script p]63mc (70)
II[2] [script p]6 (c' = 1/2c) (53)








































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