[script p]3m1 3m1 Trigonal
No. 49 [script p]3m1 Patterson symmetry [script p]-3m1
FIRST SETTING

symmetry group diagram

Origin on 3m1

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

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)  m   x-xz
      (mxy | 0, 0, 0)
(5)  m   x, 2xz
      (mx | 0, 0, 0)
(6)  m   2xxz
      (my | 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(3) -x + y-xz
(4) -y-xz(5) -x + yyz(6) xx - yz
no conditions
  Special: no extra conditions
3 b  . m . 
x-xzx, 2xz-(2x), -xz
1 a  3 m . 
0, 0, z

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]1
a' = c   
Origin at x, 0, 0
Along [210]   [script p]11m
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]1m1 ([script p]m11, 4)1; 4
 [3] [script p]1m1 ([script p]m11, 4)1; 5
 [3] [script p]1m1 ([script p]m11, 4)1; 6
IIa none
IIb[2] [script p]3c1 (c' = 2c) (50)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]3m1 (c' = 2c) (49)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]-31m (51); [2] [script p]6mm (68); [2] [script p]63mc (70); [2] [script p]-6m2 (71)
IInone
[script p]31m 31m Trigonal
No. 49 [script p]31m Patterson symmetry [script p]-31m
SECOND SETTING

symmetry group diagram

Origin on 31m

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

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)  m   xxz
      (m3 | 0, 0, 0)
(5)  m   x, 0, z
      (m2 | 0, 0, 0)
(6)  m   0, yz
      (m1 | 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(3) -x + y-xz
(4) yxz(5) x - y-yz(6) -x-x + yz
no conditions
  Special: no extra conditions
3 b  . . m 
x, 0, z0, xz-x-xz
1 a  3 . m 
0, 0, z

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]11m
a' = c   
Origin at x, 0, 0
Along [210]   [script p]1
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]11m ([script p]m11, 4)1; 4
 [3] [script p]11m ([script p]m11, 4)1; 5
 [3] [script p]11m ([script p]m11, 4)1; 6
IIa none
IIb[2] [script p]31c (c' = 2c) ([script p]3c1, 50)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]31m (c' = 2c) ([script p]3m1, 49)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]-31m (51); [2] [script p]6mm (68); [2] [script p]63mc (70); [2] [script p]-6m2 (71)
IInone








































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