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Input space group symbol: H 61
Convention: Hall symbol

Number of lattice translations: 3
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 6
Total number of symmetry operations: 18

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---
x-y,x,z+1/6 6^1[0,0,1]0,0,1/60,0,0
-y,x-y,z+1/3 3^1[0,0,1]0,0,1/30,0,0
-x,-y,z+1/2 2[0,0,1]0,0,1/20,0,0
-x+y,-x,z+2/3 3^-1[0,0,1]0,0,2/30,0,0
y,-x+y,z+5/6 6^-1[0,0,1]0,0,5/60,0,0
x+2/3,y+1/3,z 1---
x-y+2/3,x+1/3,z+1/6 6^1[0,0,1]0,0,1/61/3,2/3,0
-y+2/3,x-y+1/3,z+1/3 3^1[0,0,1]0,0,1/31/3,1/3,0
-x+2/3,-y+1/3,z+1/2 2[0,0,1]0,0,1/21/3,1/6,0
-x+y+2/3,-x+1/3,z+2/3 3^-1[0,0,1]0,0,2/31/3,0,0
y+2/3,-x+y+1/3,z+5/6 6^-1[0,0,1]0,0,5/61/3,-1/3,0
x+1/3,y+2/3,z 1---
x-y+1/3,x+2/3,z+1/6 6^1[0,0,1]0,0,1/6-1/3,1/3,0
-y+1/3,x-y+2/3,z+1/3 3^1[0,0,1]0,0,1/30,1/3,0
-x+1/3,-y+2/3,z+1/2 2[0,0,1]0,0,1/21/6,1/3,0
-x+y+1/3,-x+2/3,z+2/3 3^-1[0,0,1]0,0,2/31/3,1/3,0
y+1/3,-x+y+2/3,z+5/6 6^-1[0,0,1]0,0,5/62/3,1/3,0

Space group number: 169
Conventional Hermann-Mauguin symbol: P 61
Universal    Hermann-Mauguin symbol: P 61 (2*a+b,-a+b,c)
Hall symbol:  P 61 (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
a181x,y,z

Harker planes:
Algebraic Normal vector A point in the plane
-y,-x-y,1/6[0,0,1]0,0,1/6
x-y,-x-2*y,1/3[0,0,1]0,0,1/3
2*x,2*y,1/2[0,0,1]0,0,1/2

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

Grid factors implied by symmetries:
  Space group: (3, 3, 6)
  Structure-seminvariant vectors and moduli: (1, 1, 1)
  Euclidean normalizer: (3, 3, 6)

  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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