[script p]6522 622 Hexagonal
No. 67 [script p]6522 Patterson symmetry [script p]6/mmm

symmetry group diagram

Origin on 2[100] at 65(2,1,1)1

Asymmetric unit 0 ≤ z ≤ 1/12

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  3+ (2/3)   0, 0, z
      (3z | 0, 0, 2/3)
(3)  3- (1/3)   0, 0, z
      (3z-1 | 0, 0, 1/3)
(4)  2 (1/2)   0, 0, z
      (2z | 0, 0, 1/2)
(5)  6- (1/6)   0, 0, z
      (6z-1 | 0, 0, 1/6)
(6)  6+ (5/6)   0, 0, z
      (6z | 0, 0, 5/6)
(7)  2   xx1/3
      (2xy | 0, 0, 2/3)
(8)  2   x, 0, 0
      (2x | 0, 0, 0)
(9)  2   0, y1/6
      (2y | 0, 0, 1/3)
(10)  2   x-x1/12
      (23 | 0, 0, 1/6)
(11)  2   x, 2x1/4
      (22 | 0, 0, 1/2)
(12)  2   2xx5/12
      (21 | 0, 0, 5/6)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
12 c 1
(1) xyz(2) -yx - yz + 2/3(3) -x + y-xz + 1/3
(4) -x-yz + 1/2(5) y-x + yz + 1/6(6) x - yxz + 5/6
(7) yx-z + 2/3(8) x - y-y-z(9) -x-x + y-z + 1/3
(10) -y-x-z + 1/6(11) -x + yy-z + 1/2(12) xx - y-z + 5/6
l: l = 6n
  Special: as above, plus
6 b  . . 2 
x, 2x3/4-(2x), -x5/12x-x1/12-x, -(2x), 1/42xx11/12-xx7/12
l: l = 2n
or l = 3n + 1
or l = 3n + 2
6 a  . 2 . 
x, 0, 00, x2/3-x-x1/3-x, 0, 1/20, -x1/6xx5/6
l: l = 2n
or l = 3n + 1
or l = 3n + 2

Symmetry of special projections

Along [001]   6mm

Origin at 0, 0, z
Along [100]   [script p]2mg
a' = c   
Origin at x, 0, 0
Along [210]   [script p]2mg
a' = c   
Origin at x1/2x5/12

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]6511 ([script p]65, 58)1; 2; 3; 4; 5; 6
 [2] [script p]3221 ([script p]3212, 48)1; 2; 3; 7; 8; 9
 [2] [script p]3212 (48)1; 2; 3; 10; 11; 12
 [3] [script p]2122 ([script p]2221, 14)1; 4; 7; 10
 [3] [script p]2122 ([script p]2221, 14)1; 4; 8; 11
 [3] [script p]2122 ([script p]2221, 14)1; 4; 9; 12
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[5] [script p]6122 (c' = 5c) (63); [7] [script p]6522 (c' = 7c) (67)

Minimal non-isotypic non-enantiomorphic supergroups


Inone
II[2] [script p]6422 (c' = 1/2c) (66); [3] [script p]6322 (c' = 1/3c) (65)








































to end of page
to top of page