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Result of symbol lookup:
  Space group number: 205
  Schoenflies symbol: Th^6
  Hermann-Mauguin symbol: P a -3
  Hall symbol: -P 2ac 2ab 3

Input space group symbol: P a -3
Convention: Default

Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 12
Total number of symmetry operations: 24

Parallelepiped containing an asymmetric unit:
  0<=x<=1/2; 0<=y<=1/4; -1/4<=z<1/4

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-x+1/2,-y,z+1/2 2[0,0,1]0,0,1/21/4,0,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
-x,y+1/2,-z+1/2 2[0,1,0]0,1/2,00,0,1/4
z,x,y 3^1[1,1,1]0,0,00,0,0
-z+1/2,-x,y+1/2 3^-1[-1,1,1]0,0,01/2,-1/2,0
z+1/2,-x+1/2,-y 3^-1[1,-1,1]0,0,01/2,0,0
-z,x+1/2,-y+1/2 3^1[-1,-1,1]0,0,00,1/2,0
y,z,x 3^-1[1,1,1]0,0,00,0,0
y+1/2,-z+1/2,-x 3^-1[-1,-1,1]1/3,1/3,-1/31/3,1/6,0
-y,z+1/2,-x+1/2 3^1[-1,1,1]-1/3,1/3,1/31/6,1/6,0
-y+1/2,-z,x+1/2 3^1[1,-1,1]1/3,-1/3,1/3-1/6,1/3,0
-x,-y,-z -1--0,0,0
x-1/2,y,-z-1/2 -2[0,0,1]-1/2,0,00,0,-1/4
-x-1/2,y-1/2,z -2[1,0,0]0,-1/2,0-1/4,0,0
x,-y-1/2,z-1/2 -2[0,1,0]0,0,-1/20,-1/4,0
-z,-x,-y -3^1[1,1,1]0,0,00,0,0
z-1/2,x,-y-1/2 -3^-1[-1,1,1]0,0,0-1/2,-1/2,0
-z-1/2,x-1/2,y -3^-1[1,-1,1]0,0,00,-1/2,-1/2
z,-x-1/2,y-1/2 -3^1[-1,-1,1]0,0,0-1/2,0,-1/2
-y,-z,-x -3^-1[1,1,1]0,0,00,0,0
-y-1/2,z-1/2,x -3^-1[-1,-1,1]0,0,00,-1/2,0
y,-z-1/2,x-1/2 -3^1[-1,1,1]0,0,00,0,-1/2
y-1/2,z,-x-1/2 -3^1[1,-1,1]0,0,0-1/2,0,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
d241x,y,z
c83x,x,x
b4-31/2,1/2,1/2
a4-30,0,0 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 1, 1) 2

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