p6 6 Hexagonal/Hexagonal
No. 73 p6 Patterson symmetry p6/m

symmetry group diagram

Origin on 6

Asymmetric unit 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 1/2; x ≤ (1 + y)/2; y ≤ min(1 - xx)
Vertices
0, 0   1/2, 0   2/31/3   1/21/2  

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)  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(1, 0, 0); t(0, 1, 0); (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-yz (5) y-x + yz (6) x - yxz
no conditions
    Special: no extra conditions
3 c  2 . . 
1/2, 0, z 0, 1/2z 1/21/2z
2 b  3 . . 
1/32/3z 2/31/3z
1 a  6 . . 
0, 0, z

Symmetry of special projections

Along [001]   p6
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]1m1
a' = 1/2(a + 2b)   
Origin at x, 0, 0
Along [210]   [script p]1m1
a' = 1/2b   
Origin at x1/2x, 0

Maximal non-isotypic subgroups


I [2] p3 (65) 1; 2; 3
  [3] p211 (p112, 3) 1; 4
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] h6 (a' = 3ab' = 3b) (p6, 73)

Minimal non-isotypic supergroups


I [2] p6/m (75); [2] p622 (76); [2] p6mm (77)
II none








































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