p6 6 Hexagonal/Hexagonal No. 73 p6 Patterson symmetry p6/m

Origin on 6

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 d 1
 (1) x, y, z (2) -y, x - y, z (3) -x + y, -x, z (4) -x, -y, z (5) y, -x + y, z (6) x - y, x, z
no conditions
Special: no extra conditions
 3 c 2 . .
 1/2, 0, z 0, 1/2, z 1/2, 1/2, z
 2 b 3 . .
 1/3, 2/3, z 2/3, 1/3, z
 1 a 6 . .
 0, 0, z

Symmetry of special projections

 Along [001]   p6 a' = a   b' = b    Origin at 0, 0, z Along [100]   1m1 a' = 1/2(a + 2b)    Origin at x, 0, 0 Along [210]   1m1 a' = 1/2b    Origin at x, 1/2x, 0

Maximal non-isotypic subgroups

 I [2] p3 (65) 1; 2; 3 [3] p211 (p112, 3) 1; 4
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] h6 (a' = 3a, b' = 3b) (p6, 73)

Minimal non-isotypic supergroups

 I [2] p6/m (75); [2] p622 (76); [2] p6mm (77)
 II none