p3m1 3m Hexagonalinfo
No. 14 p3m1 Patterson symmetry p6mm

symmetry group diagram

Origin at 3 m 1

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
6 e 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 d  . m . 
x, -xx, 2x (-2x), -x
no extra conditions
1 c  3 m . 
2/3, 1/3
no extra conditions
1 b  3 m . 
1/3, 2/3
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] p1m1 (cm, 5)1; 4
 [3] p1m1 (cm, 5)1; 5
 [3] p1m1 (cm, 5)1; 6
IIa none
IIb[3] h3m1 (a' = 3a, b' = 3b) (p31m, 15)

Maximal isomorphic subgroups of lowest index

IIc[4] p3m1 (a' = 2a, b' = 2b) (14)

Minimal non-isomorphic supergroups

I[2] p6mm (17)
II[3] h3m1 (p31m, 15)








































to end of page
to top of page