3m1 3m1 Trigonal No. 49 3m1 Patterson symmetry -3m1 FIRST SETTING

Origin on 3m1

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 c 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 b . m .
 x, -x, z x, 2x, z -(2x), -x, z
 1 a 3 m .
 0, 0, z

Symmetry of special projections

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

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 311 (3, 42) 1; 2; 3 [3] 1m1 (m11, 4) 1; 4 [3] 1m1 (m11, 4) 1; 5 [3] 1m1 (m11, 4) 1; 6
 IIa none
 IIb [2] 3c1 (c' = 2c) (50)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 3m1 (c' = 2c) (49)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31m (51); [2] 6mm (68); [2] 63mc (70); [2] -6m2 (71)
 II none
 31m 31m Trigonal No. 49 31m Patterson symmetry -31m SECOND SETTING

Origin on 31m

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 6 c 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 b . . m
 x, 0, z 0, x, z -x, -x, z
 1 a 3 . m
 0, 0, z

Symmetry of special projections

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

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 311 (3, 42) 1; 2; 3 [3] 11m (m11, 4) 1; 4 [3] 11m (m11, 4) 1; 5 [3] 11m (m11, 4) 1; 6
 IIa none
 IIb [2] 31c (c' = 2c) (3c1, 50)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 31m (c' = 2c) (3m1, 49)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] -31m (51); [2] 6mm (68); [2] 63mc (70); [2] -6m2 (71)
 II none