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Result of symbol lookup:
  Space group number: 164
  Schoenflies symbol: D3d^3
  Hermann-Mauguin symbol: P -3 m 1
  Hall symbol: -P 3 2"

Input space group symbol: P -3 m 1
Convention: Default

Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 6
Total number of symmetry operations: 12

Parallelepiped containing an asymmetric unit:
  0<=x<=1/2; -1/3<=y<=0; 0<=z<1

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[0,1,0]0,0,00,0,0
x-y,-y,-z 2[1,0,0]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[0,1,0]0,0,00,0,0
-x+y,y,z -2[1,0,0]0,0,00,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
j121x,y,z
i6mx,-x,z
h62x,0,1/2
g62x,0,0
f32/m1/2,0,1/2
e32/m1/2,0,0
d23m1/3,-1/3,z
c23m0,0,z
b1-3m0,0,1/2
a1-3m0,0,0

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
2*x,x,2*z[0,1,0]0,0,0
y,2*y,2*z[1,0,0]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: (1, 1, 1)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (1, 1, 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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