[script p]312 312 Trigonal
No. 46 [script p]312 Patterson symmetry [script p]-31m
FIRST SETTING

symmetry group diagram

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, 1/2x, 2x, 1/2-(2x), -x, 1/2
3 d  . . 2 
x, -x, 0x, 2x, 0-(2x), -x, 0
2 c  3 . . 
0, 0, z0, 0, -z
1 b  3 . 2 
0, 0, 1/2
1 a  3 . 2 
0, 0, 0

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z 		Along [100]   [script p]1m1
a' = c   
Origin at x, 0, 0 		Along [210]   [script p]211
a' = c   
Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

IIc[2] [script p]312 (c' = 2c) (46)

Minimal non-isotypic non-enantiomorphic supergroups

I[2] [script p]-31m (51); [2] [script p]-31c (52); [2] [script p]622 (62); [2] [script p]6322 (65); [2] [script p]-6m2 (71); [2] [script p]-6c2 (72)
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[script p]321 321 Trigonal
No. 46 [script p]321 Patterson symmetry [script p]-3m1
SECOND SETTING

symmetry group diagram

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, 1/20, x, 1/2-x, -x, 1/2
3 d  . 2 . 
x, 0, 00, x, 0-x, -x, 0
2 c  3 . . 
0, 0, z0, 0, -z
1 b  3 2 . 
0, 0, 1/2
1 a  3 2 . 
0, 0, 0

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z 		Along [100]   [script p]211
a' = c   
Origin at x, 0, 0 		Along [210]   [script p]1m1
a' = c   
Origin at x, 1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups

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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

IIc[2] [script p]321 (c' = 2c) ([script p]312, 46)

Minimal non-isotypic non-enantiomorphic supergroups

I[2] [script p]-31m (51); [2] [script p]-31c (52); [2] [script p]622 (62); [2] [script p]6322 (65); [2] [script p]-6m2 (71); [2] [script p]-6c2 (72)
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