p3 3 Trigonal/Hexagonal No. 65 p3 Patterson symmetry p-3

Origin on 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       (1 | 0, 0, 0) (2)  3+   0, 0, z       (3z | 0, 0, 0) (3)  3-   0, 0, z       (3z-1 | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

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

Symmetry of special projections

 Along [001]   p3 a' = a   b' = b    Origin at 0, 0, z Along [100]   111 a' = 1/2(a + 2b)    Origin at x, 0, 0 Along [210]   111 a' = 1/2b    Origin at x, 1/2x, 0

Maximal non-isotypic subgroups

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

Maximal isotypic subgroups of lowest index

 IIc [3] h3 (a' = 3a, b' = 3b) (p3, 65)

Minimal non-isotypic supergroups

 I [2] p-3 (66); [2] p312 (67); [2] p321 (68); [2] p3m1 (69); [2] p31m (70); [2] p6 (73); [2] p-6 (74)
 II none