[script p]3c1 3m1 Trigonal
No. 50 [script p]3c1 Patterson symmetry [script p]-3m1
FIRST SETTING

symmetry group diagram

Origin on 3c1

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)  c   x-xz
      (mxy | 0, 0, 1/2)
(5)  c   x, 2xz
      (mx | 0, 0, 1/2)
(6)  c   2xxz
      (my | 0, 0, 1/2)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
6 b 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) -y-xz + 1/2(5) -x + yyz + 1/2(6) xx - yz + 1/2
l: l = 2n
  Special: no extra conditions
2 a  3 . . 
0, 0, z0, 0, z + 1/2

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]1
a' = 1/2c   
Origin at x, 0, 0
Along [210]   [script p]11g
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]1c1 ([script p]c11, 5)1; 4
 [3] [script p]1c1 ([script p]c11, 5)1; 5
 [3] [script p]1c1 ([script p]c11, 5)1; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]3c1 (c' = 3c) (50)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]-31c (52); [2] [script p]6cc (69); [2] [script p]63mc (70); [2] [script p]-6c2 (72)
II[2] [script p]3m1 (c' = 1/2c) (49)
[script p]31c 31m Trigonal
No. 50 [script p]31c Patterson symmetry [script p]-31m
SECOND SETTING

symmetry group diagram

Origin on 31c

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)  c   xxz
      (m3 | 0, 0, 1/2)
(5)  c   x, 0, z
      (m2 | 0, 0, 1/2)
(6)  c   0, yz
      (m1 | 0, 0, 1/2)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
6 b 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) yxz + 1/2(5) x - y-yz + 1/2(6) -x-x + yz + 1/2
l: l = 2n
  Special: no extra conditions
2 a  3 . . 
0, 0, z0, 0, z + 1/2

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]11g
a' = c   
Origin at x, 0, 0
Along [210]   [script p]1
a' = 1/2c   
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]11c ([script p]c11, 5)1; 4
 [3] [script p]11c ([script p]c11, 5)1; 5
 [3] [script p]11c ([script p]c11, 5)1; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]31c (c' = 3c) ([script p]3c1, 50)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]-31c (52); [2] [script p]6cc (69); [2] [script p]63mc (70); [2] [script p]-6c2 (72)
II[2] [script p]3m1 (c' = 1/2c) (49)








































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