p-3 -3 Trigonal/Hexagonal No. 66 p-3 Patterson symmetry p-3

Origin at centre (-3)

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

Symmetry operations

 (1)  1 (2)  3+   0, 0, z (3)  3-   0, 0, z (4)  -1   0, 0, 0 (5)  -3+   0, 0, z; 0, 0, 0 (6)  -3-   0, 0, z; 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 e 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 d -1
 1/2, 0, 0 0, 1/2, 0 1/2, 1/2, 0
 2 c 3 . .
 1/3, 2/3, z 2/3, 1/3, -z
 2 b 3 . .
 0, 0, z 0, 0, -z
 1 a -3 . .
 0, 0, 0

Symmetry of special projections

 Along [001]   p6 a' = a   b' = b    Origin at 0, 0, z Along [100]   211 a' = 1/2(a + 2b)    Origin at x, 0, 0 Along [210]   211 a' = 1/2b    Origin at x, 1/2x, 0

Maximal non-isotypic subgroups

 I [2] p3 (65) 1; 2; 3 [3] p-1 (2) 1; 4
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [3] h-3 (a' = 3a, b' = 3b) (p-3, 66)

Minimal non-isotypic supergroups

 I [2] p-31m (71); [2] p-3m1 (72); [2] p6/m (75)
 II none