[script p]63 6 Hexagonal
No. 56 [script p]63 Patterson symmetry [script p]6/m

symmetry group diagram

Origin on 3 on 63

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1; y ≤ x

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
6 b 1
(1) x, y, z(2) -y, x - y, z(3) -x + y, -x, z
(4) -x, -y, z + 1/2(5) y, -x + y, z + 1/2(6) x - y, x, z + 1/2
l: l = 2n
  Special: no extra conditions
2 a  3 . . 
0, 0, z0, 0, z + 1/2

Symmetry of special projections

Along [001]   6

Origin at 0, 0, z 		Along [100]   [script p]11g
a' = c   
Origin at x, 0, 0 		Along [210]   [script p]11g
a' = c   
Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

I[2] [script p]3 (42)1; 2; 3
 [3] [script p]1121 (9)1; 4
IIa none
IIb[3] [script p]65 (c' = 3c) (58); [3] [script p]61 (c' = 3c) (54)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

IIc[3] [script p]63 (c' = 3c) (56)

Minimal non-isotypic non-enantiomorphic supergroups

I[2] [script p]63/m (61); [2] [script p]6322 (65); [2] [script p]63mc (70)
II[2] [script p]6 (c' = 1/2c) (53)








































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