p3m1 3m Hexagonal No. 14 p3m1 Patterson symmetry p6mm

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, -x x, 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
 [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)