[script p]65 6 Hexagonal
No. 58 [script p]65 Patterson symmetry [script p]6/m

symmetry group diagram

Origin on 65

Asymmetric unit 0 ≤ z ≤ 1/6

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
6 a 1
(1) xyz(2) -yx - yz + 2/3(3) -x + y-xz + 1/3
(4) -x-yz + 1/2(5) y-x + yz + 1/6(6) x - yxz + 5/6
l: l = 6n

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]32 (44)1; 2; 3
 [3] [script p]1121 (9)1; 4
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[5] [script p]61 (c' = 5c) (54); [7] [script p]65 (c' = 7c) (58)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6522 (67)
II[2] [script p]64 (c' = 1/2c) (57); [3] [script p]63 (c' = 1/3c) (56)








































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