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Input space group symbol: -H 3 2
Convention: Hall symbol

Number of lattice translations: 3
Space group is centric.
Number of representative symmetry operations: 6
Total number of symmetry operations: 36

Parallelepiped containing an asymmetric unit:
  cctbx Error: Brick is not available for the given space group representation.

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y,x-y,z 3^1[0,0,1]0,0,00,0,0
-x+y,-x,z 3^-1[0,0,1]0,0,00,0,0
-y,-x,-z 2[-1,1,0]0,0,00,0,0
x,x-y,-z 2[2,1,0]0,0,00,0,0
-x+y,y,-z 2[1,2,0]0,0,00,0,0
-x,-y,-z -1--0,0,0
y,-x+y,-z -3^1[0,0,1]0,0,00,0,0
x-y,x,-z -3^-1[0,0,1]0,0,00,0,0
y,x,z -2[-1,1,0]0,0,00,0,0
-x,-x+y,z -2[2,1,0]0,0,00,0,0
x-y,-y,z -2[1,2,0]0,0,00,0,0
x+2/3,y+1/3,z 1---
-y+2/3,x-y+1/3,z 3^1[0,0,1]0,0,01/3,1/3,0
-x+y+2/3,-x+1/3,z 3^-1[0,0,1]0,0,01/3,0,0
-y+2/3,-x+1/3,-z 2[-1,1,0]1/6,-1/6,01/2,0,0
x+2/3,x-y+1/3,-z 2[2,1,0]2/3,1/3,00,0,0
-x+y+2/3,y+1/3,-z 2[1,2,0]1/6,1/3,01/4,0,0
-x+2/3,-y+1/3,-z -1--1/3,1/6,0
y+2/3,-x+y+1/3,-z -3^1[0,0,1]0,0,01/3,-1/3,0
x-y+2/3,x+1/3,-z -3^-1[0,0,1]0,0,01/3,2/3,0
y+2/3,x+1/3,z -2[-1,1,0]1/2,1/2,01/6,0,0
-x+2/3,-x+y+1/3,z -2[2,1,0]0,0,01/3,0,0
x-y+2/3,-y+1/3,z -2[1,2,0]1/2,0,00,1/6,0
x+1/3,y+2/3,z 1---
-y+1/3,x-y+2/3,z 3^1[0,0,1]0,0,00,1/3,0
-x+y+1/3,-x+2/3,z 3^-1[0,0,1]0,0,01/3,1/3,0
-y+1/3,-x+2/3,-z 2[-1,1,0]-1/6,1/6,01/2,0,0
x+1/3,x-y+2/3,-z 2[2,1,0]1/3,1/6,0-1/2,0,0
-x+y+1/3,y+2/3,-z 2[1,2,0]1/3,2/3,00,0,0
-x+1/3,-y+2/3,-z -1--1/6,1/3,0
y+1/3,-x+y+2/3,-z -3^1[0,0,1]0,0,02/3,1/3,0
x-y+1/3,x+2/3,-z -3^-1[0,0,1]0,0,0-1/3,1/3,0
y+1/3,x+2/3,z -2[-1,1,0]1/2,1/2,0-1/6,0,0
-x+1/3,-x+y+2/3,z -2[2,1,0]0,1/2,01/6,0,0
x-y+1/3,-y+2/3,z -2[1,2,0]0,0,00,1/3,0 

Space group number: 164
Conventional Hermann-Mauguin symbol: P -3 m 1
Universal    Hermann-Mauguin symbol: P -3 m 1 (2*a+b,-a+b,c)
Hall symbol: -P 3 2" (1/3*x+1/3*y,-1/3*x+2/3*y,z)
Change-of-basis matrix: 2*x-y,x+y,z
               Inverse: 1/3*x+1/3*y,-1/3*x+2/3*y,z

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
j361x,y,z
i18m0,y,z
h182x,-x,1/2
g182x,-x,0
f92/m1/6,-1/6,1/2
e92/m1/6,-1/6,0
d63m0,-1/3,z
c63m0,0,z
b3-3m0,0,1/2
a3-3m0,0,0 

Harker planes:
Algebraic Normal vector A point in the plane
x-y,-x-2*y,0[0,0,1]0,0,0
x+y,x+y,2*z[-1,1,0]0,0,0
0,x-2*y,2*z[2,1,0]0,0,0
2*x+y,0,2*z[1,2,0]0,0,0 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2
  Further generators:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
-x,-y,z 2[0,0,1]0,0,00,0,0 

Grid factors implied by symmetries:
  Space group: (3, 3, 1)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (3, 3, 2)

  All points of a grid over the unit cell are mapped
  exactly onto other grid points only if the factors
  shown above are factors of the grid.
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