[script p]6/m 6/m Hexagonal
No. 60 [script p]6/m Patterson symmetry [script p]6/m

symmetry group diagram

Origin at centre (6/m)

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1/2; 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   0, 0, z
      (2z | 0, 0, 0)
(5)  6-   0, 0, z
      (6z-1 | 0, 0, 0)
(6)  6+   0, 0, z
      (6z | 0, 0, 0)
(7)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(8)  -3+   0, 0, z; 0, 0, 0
      (-3z | 0, 0, 0)
(9)  -3-   0, 0, z; 0, 0, 0
      (-3z-1 | 0, 0, 0)
(10)  m   xy, 0
      (mz | 0, 0, 0)
(11)  -6-   0, 0, z; 0, 0, 0
      (-6z-1 | 0, 0, 0)
(12)  -6+   0, 0, z; 0, 0, 0
      (-6z | 0, 0, 0)

Generators selected (1); t(0, 0, 1); (2); (4); (7)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
12 f 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) -x-yz(5) y-x + yz(6) x - yxz
(7) -x-y-z(8) y-x + y-z(9) x - yx-z
(10) xy-z(11) -yx - y-z(12) -x + y-x-z
no conditions
  Special: no extra conditions
6 e  m . . 
xy1/2-yx - y1/2-x + y-x1/2-x-y1/2y-x + y1/2x - yx1/2
6 d  m . . 
xy, 0-yx - y, 0-x + y-x, 0-x-y, 0y-x + y, 0x - yx, 0
2 c  6 . . 
0, 0, z0, 0, -z
1 b  6/m . . 
0, 0, 1/2
1 a  6/m . . 
0, 0, 0

Symmetry of special projections

Along [001]   6

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

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]-6 (59)1; 2; 3; 10; 11; 12
 [2] [script p]6 (53)1; 2; 3; 4; 5; 6
 [2] [script p]-3 (45)1; 2; 3; 7; 8; 9
 [3] [script p]112/m (11)1; 4; 7; 10
IIa none
IIb[2] [script p]63/m (c' = 2c) (61)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]6/m (c' = 2c) (60)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6/mmm (73); [2] [script p]6/mcc (74)
IInone








































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