-3 -3 Trigonal No. 45 -3 Patterson symmetry -3

Origin at centre (-3)

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

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)  -1   0, 0, 0      (-1 | 0, 0, 0) (5)  -3+   0, 0, z; 0, 0, 0      (-3z | 0, 0, 0) (6)  -3-   0, 0, z; 0, 0, 0      (-3z-1 | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 d 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
no conditions
Special: no extra conditions
 2 c 3 . .
 0, 0, z 0, 0, -z
 1 b -3 . .
 0, 0, 1/2
 1 a -3 . .
 0, 0, 0

Symmetry of special projections

 Along [001]   6Origin at 0, 0, z Along [100]   211a' = c   Origin at x, 0, 0 Along [210]   211a' = c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 3 (42) 1; 2; 3 [3] -1 (2) 1; 4
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] -3 (c' = 2c) (45)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31m (51); [2] -31c (52); [2] 6/m (60); [2] 63/m (61)
 II none