[script p]3112 312 Trigonal
No. 47 [script p]3112 Patterson symmetry [script p]-31m
FIRST SETTING

symmetry group diagram

Origin on 2[210] at 311(1,1,2)

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  3+ (1/3)   0, 0, z
      (3z | 0, 0, 1/3)
(3)  3- (2/3)   0, 0, z
      (3z-1 | 0, 0, 2/3)
(4)  2   x-x1/3
      (23 | 0, 0, 2/3)
(5)  2   x, 2x1/6
      (22 | 0, 0, 1/3)
(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 c 1
(1) xyz(2) -yx - yz + 1/3(3) -x + y-xz + 2/3
(4) -y-x-z + 2/3(5) -x + yy-z + 1/3(6) xx - y-z
l: l = 3n
  Special: no extra conditions
3 b  . . 2 
x-x5/6x, 2x1/6-(2x), -x1/2
3 a  . . 2 
x-x1/3x, 2x2/3-(2x), -x, 0

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]1m1
a' = c   
Origin at x, 0, 1/6
Along [210]   [script p]211
a' = c   
Origin at x1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]3111 ([script p]31, 43)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
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


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

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6122 (63); [2] [script p]6422 (66)
II[3] [script p]312 (c' = 1/3c) (46)
[script p]3121 321 Trigonal
No. 47 [script p]3121 Patterson symmetry [script p]-3m1
SECOND SETTING

symmetry group diagram

Origin on 2[110] at 31(1,1,2)1

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  3+ (1/3)   0, 0, z
      (3z | 0, 0, 1/3)
(3)  3- (2/3)   0, 0, z
      (3z-1 | 0, 0, 2/3)
(4)  2   xx, 0
      (2xy | 0, 0, 0)
(5)  2   x, 0, 1/3
      (2x | 0, 0, 2/3)
(6)  2   0, y1/6
      (2y | 0, 0, 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) xyz(2) -yx - yz + 1/3(3) -x + y-xz + 2/3
(4) yx-z(5) x - y-y-z + 2/3(6) -x-x + y-z + 1/3
l: l = 3n
  Special: no extra conditions
3 b  . 2 . 
x, 0, 5/60, x1/6-x-x1/2
3 a  . 2 . 
x, 0, 1/30, x2/3-x-x, 0

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]211
a' = c   
Origin at x, 0, 1/3
Along [210]   [script p]1m1
a' = c   
Origin at x1/2x1/6

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]3111 ([script p]31, 43)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
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


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

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6122 (63); [2] [script p]6422 (66)
II[3] [script p]312 (c' = 1/3c) (46)








































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