-6 -6 Hexagonal No. 59 -6 Patterson symmetry 6/m

Origin at -6

 Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 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) (4)  m   x, y, 0      (mz | 0, 0, 0) (5)  -6-   0, 0, z; 0, 0, 0      (-6z-1 | 0, 0, 0) (6)  -6+   0, 0, z; 0, 0, 0      (-6z | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 f 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 e m . .
 x, y, 1/2 -y, x - y, 1/2 -x + y, -x, 1/2
 3 d m . .
 x, y, 0 -y, x - y, 0 -x + y, -x, 0
 2 c 3 . .
 0, 0, z 0, 0, -z
 1 b -6 . .
 0, 0, 1/2
 1 a -6 . .
 0, 0, 0

Symmetry of special projections

 Along [001]   3Origin at 0, 0, z Along [100]   1m1a' = c   Origin at x, 0, 0 Along [210]   1m1a' = c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 3 (42) 1; 2; 3 [3] 11m (10) 1; 4
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] -6 (c' = 2c) (59)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] 6/m (60); [2] 63/m (61); [2] -6m2 (71); [2] -6c2 (72)
 II none