63 6 Hexagonal No. 56 63 Patterson symmetry 6/m

Origin on 3 on 63

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

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

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, z 0, 0, z + 1/2

Symmetry of special projections

 Along [001]   6Origin at 0, 0, z Along [100]   11ga' = c   Origin at x, 0, 0 Along [210]   11ga' = c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 63 (c' = 3c) (56)

Minimal non-isotypic non-enantiomorphic supergroups

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