6cc 6mm Hexagonal No. 69 6cc Patterson symmetry 6/mmm

Origin on 6cc

 Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1/2; y ≤ x

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 12 b 1
 (1) x, y, z (2) -y, x - y, z (3) -x + y, -x, z (4) -x, -y, z (5) y, -x + y, z (6) x - y, x, z (7) -y, -x, z + 1/2 (8) -x + y, y, z + 1/2 (9) x, x - y, z + 1/2 (10) y, x, z + 1/2 (11) x - y, -y, z + 1/2 (12) -x, -x + y, z + 1/2
l: l = 2n
Special: no extra conditions
 2 a 6 . .
 0, 0, z 0, 0, z + 1/2

Symmetry of special projections

 Along [001]   6mmOrigin at 0, 0, z Along [100]   11ma' = 1/2c   Origin at x, 0, 0 Along [210]   11ma' = 1/2c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 611 (6, 53) 1; 2; 3; 4; 5; 6 [2] 3c1 (50) 1; 2; 3; 7; 8; 9 [2] 31c (3c1, 50) 1; 2; 3; 10; 11; 12 [3] 2cc (cc2, 16) 1; 4; 7; 10 [3] 2cc (cc2, 16) 1; 4; 8; 11 [3] 2cc (cc2, 16) 1; 4; 9; 12
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 6cc (c' = 3c) (69)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] 6/mcc (74)
 II [2] 6mm (c' = 1/2c) (68)