[script p]6mm 6mm Hexagonal
No. 68 [script p]6mm Patterson symmetry [script p]6/mmm

symmetry group diagram

Origin on 6mm

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1; y ≤ x/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)  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)  m   x-xz
      (mxy | 0, 0, 0)
(8)  m   x, 2xz
      (mx | 0, 0, 0)
(9)  m   2xxz
      (my | 0, 0, 0)
(10)  m   xxz
      (m3 | 0, 0, 0)
(11)  m   x, 0, z
      (m2 | 0, 0, 0)
(12)  m   0, yz
      (m1 | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
12 d 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) -x-yz(5) y-x + yz(6) x - yxz
(7) -y-xz(8) -x + yyz(9) xx - yz
(10) yxz(11) x - y-yz(12) -x-x + yz
no conditions
  Special: no extra conditions
6 c  . m . 
x-xzx, 2xz-(2x), -xz-xxz-x, -(2x), z2xxz
6 b  . . m 
x, 0, z0, xz-x-xz-x, 0, z0, -xzxxz
1 a  6 m m 
0, 0, z

Symmetry of special projections

Along [001]   6mm

Origin at 0, 0, z
Along [100]   [script p]11m
a' = c   
Origin at x, 0, 0
Along [210]   [script p]11m
a' = c   
Origin at x1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]611 ([script p]6, 53)1; 2; 3; 4; 5; 6
 [2] [script p]3m1 (49)1; 2; 3; 7; 8; 9
 [2] [script p]31m ([script p]3m1, 49)1; 2; 3; 10; 11; 12
 [3] [script p]2mm ([script p]mm2, 15)1; 4; 7; 10
 [3] [script p]2mm ([script p]mm2, 15)1; 4; 8; 11
 [3] [script p]2mm ([script p]mm2, 15)1; 4; 9; 12
IIa none
IIb[2] [script p]63mc (c' = 2c) (70); [2] [script p]63cm (c' = 2c) ([script p]63mc, 70); [2] [script p]6cc (c' = 2c) (69)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]6mm (c' = 2c) (68)

Minimal non-isotypic non-enantiomorphic supergroups


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








































to end of page
to top of page