3c1 3m1 Trigonal No. 50 3c1 Patterson symmetry -3m1 FIRST SETTING

Origin on 3c1

 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)  c   x, -x, z (5)  c   x, 2x, z (6)  c   2x, x, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

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

Symmetry of special projections

 Along [001]   3mOrigin at 0, 0, z Along [100]   1a' = 1/2c   Origin at x, 0, 0 Along [210]   11ga' = c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 311 (3, 42) 1; 2; 3 [3] 1c1 (c11, 5) 1; 4 [3] 1c1 (c11, 5) 1; 5 [3] 1c1 (c11, 5) 1; 6
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 3c1 (c' = 3c) (50)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31c (52); [2] 6cc (69); [2] 63mc (70); [2] -6c2 (72)
 II [2] 3m1 (c' = 1/2c) (49)
 31c 31m Trigonal No. 50 31c Patterson symmetry -31m SECOND SETTING

Origin on 31c

 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)  c   x, x, z (5)  c   x, 0, z (6)  c   0, y, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

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

Symmetry of special projections

 Along [001]   3mOrigin at 0, 0, z Along [100]   11ga' = c   Origin at x, 0, 0 Along [210]   1a' = 1/2c   Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 311 (3, 42) 1; 2; 3 [3] 11c (c11, 5) 1; 4 [3] 11c (c11, 5) 1; 5 [3] 11c (c11, 5) 1; 6
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 31c (c' = 3c) (3c1, 50)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31c (52); [2] 6cc (69); [2] 63mc (70); [2] -6c2 (72)
 II [2] 3m1 (c' = 1/2c) (49)