p31m 3m Hexagonalinfo
No. 15 p31m Patterson symmetry p6mm

symmetry group diagram

Origin at 3 1 m

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)  m   x, x(5)  m   x, 0(6)  m   0, y

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) y, x(5) x - y, -y(6) -x, -x + y
no conditions
    Special: as above, plus
3 c  . . m 
x, 0 0, x -x, -x
no extra conditions
2 b  3 . . 
1/3, 2/3 2/3, 1/3
no extra conditions
1 a  3 . m 
0, 0
no extra conditions

Maximal non-isomorphic subgroups

I[2] p311 (p3, 13)1; 2; 3
 brace[3] p11m (cm, 5)1; 4
 [3] p11m (cm, 5)1; 5
 [3] p11m (cm, 5)1; 6
IIa none
IIb[3] h31m (a' = 3a, b' = 3b) (p3m1, 14)

Maximal isomorphic subgroups of lowest index

IIc[4] p31m (a' = 2a, b' = 2b) (15)

Minimal non-isomorphic supergroups

I[2] p6mm (17)
II[3] h31m (p3m1, 14)








































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