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Input space group symbol: H -6
Convention: Hall symbol

Number of lattice translations: 3
Space group is acentric.
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 -6^1[0,0,1]0,0,00,0,0
-y,x-y,z 3^1[0,0,1]0,0,00,0,0
x,y,-z -2[0,0,1]0,0,00,0,0
-x+y,-x,z 3^-1[0,0,1]0,0,00,0,0
-y,x-y,-z -6^-1[0,0,1]0,0,00,0,0
x+2/3,y+1/3,z 1---
-x+y+2/3,-x+1/3,-z -6^1[0,0,1]0,0,01/3,0,0
-y+2/3,x-y+1/3,z 3^1[0,0,1]0,0,01/3,1/3,0
x+2/3,y+1/3,-z -2[0,0,1]2/3,1/3,00,0,0
-x+y+2/3,-x+1/3,z 3^-1[0,0,1]0,0,01/3,0,0
-y+2/3,x-y+1/3,-z -6^-1[0,0,1]0,0,01/3,1/3,0
x+1/3,y+2/3,z 1---
-x+y+1/3,-x+2/3,-z -6^1[0,0,1]0,0,01/3,1/3,0
-y+1/3,x-y+2/3,z 3^1[0,0,1]0,0,00,1/3,0
x+1/3,y+2/3,-z -2[0,0,1]1/3,2/3,00,0,0
-x+y+1/3,-x+2/3,z 3^-1[0,0,1]0,0,01/3,1/3,0
-y+1/3,x-y+2/3,-z -6^-1[0,0,1]0,0,00,1/3,0

Space group number: 174
Conventional Hermann-Mauguin symbol: P -6
Universal    Hermann-Mauguin symbol: P -6 (2*a+b,-a+b,c)
Hall symbol:  P -6 (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
l181x,y,z
k9mx,y,1/2
j9mx,y,0
i630,1/3,z
h630,-1/3,z
g630,0,z
f3-60,1/3,1/2
e3-60,1/3,0
d3-60,-1/3,1/2
c3-60,-1/3,0
b3-60,0,1/2
a3-60,0,0

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (2, 0, 3) 6
  Inversion through a centre at: 0,0,0
  Further generators:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,x-y,z -2[0,1,0]0,0,00,0,0

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