[script p]64 6 Hexagonal
No. 57 [script p]64 Patterson symmetry [script p]6/m

symmetry group diagram

Origin on 2 on 64

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

Symmetry operations

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

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 + 1/3(3) -x + y-xz + 2/3
(4) -x-yz(5) y-x + yz + 1/3(6) x - yxz + 2/3
l: l = 3n
  Special: no extra conditions
3 a  2 . . 
0, 0, z0, 0, z + 1/30, 0, z + 2/3

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]31 (43)1; 2; 3
 [3] [script p]112 (8)1; 4
IIa none
IIb[2] [script p]65 (c' = 2c) (58)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]62 (c' = 2c) (55); [7] [script p]64 (c' = 7c) (57)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6422 (66)
II[3] [script p]6 (c' = 1/3c) (53)








































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