[script p]-6 -6 Hexagonal
No. 59 [script p]-6 Patterson symmetry [script p]6/m

symmetry group diagram

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   xy, 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) xyz(2) -yx - yz(3) -x + y-xz
(4) xy-z(5) -yx - y-z(6) -x + y-x-z
no conditions
  Special: no extra conditions
3 e  m . . 
xy1/2-yx - y1/2-x + y-x1/2
3 d  m . . 
xy, 0-yx - y, 0-x + y-x, 0
2 c  3 . . 
0, 0, z0, 0, -z
1 b  -6 . . 
0, 0, 1/2
1 a  -6 . . 
0, 0, 0

Symmetry of special projections

Along [001]   3

Origin at 0, 0, z
Along [100]   [script p]1m1
a' = c   
Origin at x, 0, 0
Along [210]   [script p]1m1
a' = c   
Origin at x1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups


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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]-6 (c' = 2c) (59)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6/m (60); [2] [script p]63/m (61); [2] [script p]-6m2 (71); [2] [script p]-6c2 (72)
IInone








































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