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Result of symbol lookup:
  Space group number: 158
  Schoenflies symbol: C3v^3
  Hermann-Mauguin symbol: P 3 c 1
  Hall symbol: P 3 -2"c

Input space group symbol: P 3 c 1
Convention: Default

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

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

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+1/2 -2[1,1,0]0,0,1/20,0,0
x,x-y,z+1/2 -2[0,1,0]0,0,1/20,0,0
-x+y,y,z+1/2 -2[1,0,0]0,0,1/20,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
d61x,y,z
c23-1/3,1/3,z
b231/3,-1/3,z
a230,0,z

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: 2
    Vector    Modulus
    (0, 0, 1) 0
    (1, 2, 0) 3
  Inversion through a centre at: 0,0,0
  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, 2)
  Structure-seminvariant vectors and moduli: (3, 3, 1)
  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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