6522 622 Hexagonal No. 67 6522 Patterson symmetry 6/mmm

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, 5/12 x, -x, 1/12 -x, -(2x), 1/4 2x, x, 11/12 -x, x, 7/12
l: l = 2n
or l = 3n + 1
or l = 3n + 2
 6 a . 2 .
 x, 0, 0 0, x, 2/3 -x, -x, 1/3 -x, 0, 1/2 0, -x, 1/6 x, x, 5/6
l: l = 2n
or l = 3n + 1
or l = 3n + 2

Symmetry of special projections

 Along [001]   6mmOrigin at 0, 0, z Along [100]   2mga' = c   Origin at x, 0, 0 Along [210]   2mga' = c   Origin at x, 1/2x, 5/12

Maximal non-isotypic non-enantiomorphic subgroups

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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

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

Minimal non-isotypic non-enantiomorphic supergroups

 I none
 II [2] 6422 (c' = 1/2c) (66); [3] 6322 (c' = 1/3c) (65)