p3 3 Hexagonalinfo
No. 13 p3 Patterson symmetry p6

symmetry group diagram

Origin at 3

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

Symmetry operations

(1)  1   (2)  3+   0, 0(3)  3-   0, 0 

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

Positions

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

Maximal non-isomorphic subgroups

I[3] p1 (1)1
IIa none
IIbnone

Maximal isomorphic subgroups of lowest index

IIc[3] h3 (a' = 3a, b' = 3b) (p3, 13)

Minimal non-isomorphic supergroups

I[2] p3m1 (14); [2] p31m (15); [2] p6 (16)
IInone








































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