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

symmetry group diagram

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   2/31/3   1/32/3   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) xyz (2) -yx - yz (3) -x + y-xz
no conditions
    Special: no extra conditions
1 c  3 . . 
2/31/3z
1 b  3 . . 
1/32/3z
1 a  3 . . 
0, 0, z

Symmetry of special projections

Along [001]   p3
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]111
a' = 1/2(a + 2b)   
Origin at x, 0, 0
Along [210]   [script p]111
a' = 1/2b   
Origin at x1/2x, 0

Maximal non-isotypic subgroups


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

Maximal isotypic subgroups of lowest index


IIc [3] h3 (a' = 3ab' = 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








































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