[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   (2)  3+(2/3)   0, 0, z(3)  3-(1/3)   0, 0, z
(4)  2(1/2)   0, 0, z(5)  6-(1/6)   0, 0, z(6)  6+(5/6)   0, 0, z
(7)  2   x, x, 1/3(8)  2   x, 0, 0(9)  2   0, y, 1/6
(10)  2   x, -x, 1/12(11)  2   x, 2x, 1/4(12)  2   2x, x, 5/12

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
12 c 1
(1) x, y, z(2) -y, x - y, z + 2/3(3) -x + y, -x, z + 1/3
(4) -x, -y, z + 1/2(5) y, -x + y, z + 1/6(6) x - y, x, z + 5/6
(7) y, x, -z + 2/3(8) x - y, -y, -z(9) -x, -x + y, -z + 1/3
(10) -y, -x, -z + 1/6(11) -x + y, y, -z + 1/2(12) x, x - y, -z + 5/6
l: l = 6n
  Special: as above, plus
6 b  . . 2 
x, 2x, 3/4-(2x), -x, 5/12x, -x, 1/12-x, -(2x), 1/42x, x, 11/12-x, x, 7/12
l: l = 2n
or l = 3n + 1
or l = 3n + 2
6 a  . 2 . 
x, 0, 00, x, 2/3-x, -x, 1/3-x, 0, 1/20, -x, 1/6x, x, 5/6
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 x, 1/2x, 5/12

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)








































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