[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
      (1 | 0, 0, 0)
(2)  3+   0, 0, z
      (3z | 0, 0, 0)
(3)  3-   0, 0, z
      (3z-1 | 0, 0, 0)
(4)  2   x-x, 0
      (23 | 0, 0, 0)
(5)  2   x, 2x, 0
      (22 | 0, 0, 0)
(6)  2   2xx, 0
      (21 | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
6 f 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) -y-x-z(5) -x + yy-z(6) xx - y-z
no conditions
  Special: no extra conditions
3 e  . . 2 
x-x1/2x, 2x1/2-(2x), -x1/2
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 x1/2x, 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)
IInone
[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
      (1 | 0, 0, 0)
(2)  3+   0, 0, z
      (3z | 0, 0, 0)
(3)  3-   0, 0, z
      (3z-1 | 0, 0, 0)
(4)  2   xx, 0
      (2xy | 0, 0, 0)
(5)  2   x, 0, 0
      (2x | 0, 0, 0)
(6)  2   0, y, 0
      (2y | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
6 f 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) yx-z(5) x - y-y-z(6) -x-x + y-z
no conditions
  Special: no extra conditions
3 e  . 2 . 
x, 0, 1/20, x1/2-x-x1/2
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 x1/2x, 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)
IInone








































to end of page
to top of page