312 312 Trigonal No. 46 312 Patterson symmetry -31m FIRST SETTING

Origin at 312

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

Symmetry operations

 (1)  1 (2)  3+   0, 0, z (3)  3-   0, 0, z (4)  2   x, -x, 0 (5)  2   x, 2x, 0 (6)  2   2x, x, 0

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 f 1
 (1) x, y, z (2) -y, x - y, z (3) -x + y, -x, z (4) -y, -x, -z (5) -x + y, y, -z (6) x, x - y, -z
no conditions
Special: no extra conditions
 3 e . . 2
 x, -x, 1/2 x, 2x, 1/2 -(2x), -x, 1/2
 3 d . . 2
 x, -x, 0 x, 2x, 0 -(2x), -x, 0
 2 c 3 . .
 0, 0, z 0, 0, -z
 1 b 3 . 2
 0, 0, 1/2
 1 a 3 . 2
 0, 0, 0

Symmetry of special projections

 Along [001]   3mOrigin at 0, 0, z Along [100]   1m1a' = c   Origin at x, 0, 0 Along [210]   211a' = c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 311 (3, 42) 1; 2; 3 [3] 112 (211, 3) 1; 4 [3] 112 (211, 3) 1; 5 [3] 112 (211, 3) 1; 6
 IIa none
 IIb [3] 3212 (c' = 3c) (48); [3] 3112 (c' = 3c) (47)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 312 (c' = 2c) (46)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31m (51); [2] -31c (52); [2] 622 (62); [2] 6322 (65); [2] -6m2 (71); [2] -6c2 (72)
 II none
 321 321 Trigonal No. 46 321 Patterson symmetry -3m1 SECOND SETTING

Origin at 321

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

Symmetry operations

 (1)  1 (2)  3+   0, 0, z (3)  3-   0, 0, z (4)  2   x, x, 0 (5)  2   x, 0, 0 (6)  2   0, y, 0

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 f 1
 (1) x, y, z (2) -y, x - y, z (3) -x + y, -x, z (4) y, x, -z (5) x - y, -y, -z (6) -x, -x + y, -z
no conditions
Special: no extra conditions
 3 e . 2 .
 x, 0, 1/2 0, x, 1/2 -x, -x, 1/2
 3 d . 2 .
 x, 0, 0 0, x, 0 -x, -x, 0
 2 c 3 . .
 0, 0, z 0, 0, -z
 1 b 3 2 .
 0, 0, 1/2
 1 a 3 2 .
 0, 0, 0

Symmetry of special projections

 Along [001]   3mOrigin at 0, 0, z Along [100]   211a' = c   Origin at x, 0, 0 Along [210]   1m1a' = c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 311 (3, 42) 1; 2; 3 [3] 121 (211, 3) 1; 4 [3] 121 (211, 3) 1; 5 [3] 121 (211, 3) 1; 6
 IIa none
 IIb [3] 3221 (c' = 3c) (3212, 48); [3] 3121 (c' = 3c) (3112, 47)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 321 (c' = 2c) (312, 46)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31m (51); [2] -31c (52); [2] 622 (62); [2] 6322 (65); [2] -6m2 (71); [2] -6c2 (72)
 II none