[script p]6322 622 Hexagonal
No. 65 [script p]6322 Patterson symmetry [script p]6/mmm

symmetry group diagram

Origin at 321 at 6321

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1/4

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

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 + 1/2(5) y-x + yz + 1/2(6) x - yxz + 1/2
(7) yx-z(8) x - y-y-z(9) -x-x + y-z
(10) -y-x-z + 1/2(11) -x + yy-z + 1/2(12) xx - y-z + 1/2
l: l = 2n
  Special: no extra conditions
6 e  . . 2 
x, 2x1/4-(2x), -x1/4x-x1/4-x, -(2x), 3/42xx3/4-xx3/4
6 d  . 2 . 
x, 0, 00, x, 0-x-x, 0-x, 0, 1/20, -x1/2xx1/2
4 c  3 . . 
0, 0, z0, 0, z + 1/20, 0, -z0, 0, -z + 1/2
2 b  3 . 2 
0, 0, 1/40, 0, 3/4
2 a  3 2 . 
0, 0, 00, 0, 1/2

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 x1/2x1/4

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]6311 ([script p]63, 56)1; 2; 3; 4; 5; 6
 [2] [script p]321 ([script p]312, 46)1; 2; 3; 7; 8; 9
 [2] [script p]312 (46)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
IIb[3] [script p]6522 (c' = 3c) (67); [3] [script p]6122 (c' = 3c) (63)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]6322 (c' = 3c) (65)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]63/mmc (75)
II[2] [script p]622 (c' = 1/2c) (62)








































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