p6 6 Hexagonalinfo
No. 16 p6 Patterson symmetry p6

symmetry group diagram

Origin at 6

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
6 d 1
(1) x, y(2) -y, x - y(3) -x + y, -x
(4) -x, -y(5) y, -x + y(6) x - y, x
no conditions
    Special: as above, plus
3 c  2 . . 
1/2, 0 0, 1/2 1/2, 1/2
no extra conditions
2 b  3 . . 
1/3, 2/3 2/3, 1/3
no extra conditions
1 a  6 . . 
0, 0
no extra conditions

Maximal non-isomorphic subgroups

I[2] p3 (13)1; 2; 3
 [3] p2 (2)1; 4
IIa none
IIbnone

Maximal isomorphic subgroups of lowest index

IIc[3] h6 (a' = 3a, b' = 3b) (p6, 16)

Minimal non-isomorphic supergroups

I[2] p6mm (17)
IInone








































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