3212 312 Trigonal No. 48 3212 Patterson symmetry -31m FIRST SETTING

Origin on 2[210] at 321(1,1,2)

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

Symmetry operations

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

Symmetry of special projections

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

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 3211 (32, 44) 1; 2; 3 [3] 112 (211, 3) 1; 4 [3] 112 (211, 3) 1; 5 [3] 112 (211, 3) 1; 6
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 3112 (c' = 2c) (47); [7] 3212 (c' = 7c) (48)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] 6222 (64); [2] 6522 (67)
 II [3] 312 (c' = 1/3c) (46)
 3221 321 Trigonal No. 48 3221 Patterson symmetry -3m1 SECOND SETTING

Origin on 2[110] at 32(1,1,2)1

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

Symmetry operations

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

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

Symmetry of special projections

 Along [001]   3mOrigin at 0, 0, z Along [100]   211a' = c   Origin at x, 0, 1/6 Along [210]   1m1a' = c   Origin at x, 1/2x, 1/3

Maximal non-isotypic non-enantiomorphic subgroups

 I [2] 3211 (32, 44) 1; 2; 3 [3] 121 (211, 3) 1; 4 [3] 121 (211, 3) 1; 5 [3] 121 (211, 3) 1; 6
 IIa none
 IIb none

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [2] 3121 (c' = 2c) (3112, 47); [7] 3221 (c' = 7c) (3212, 48)

Minimal non-isotypic non-enantiomorphic supergroups

 I [2] 6222 (64); [2] 6522 (67)
 II [3] 312 (c' = 1/3c) (46)