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Result of symbol lookup:
  Space group number: 178
  Schoenflies symbol: D6^2
  Hermann-Mauguin symbol: P 61 2 2
  Hall symbol: P 61 2 (0 0 5)

Input space group symbol: P 61 2 2
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 12
Total number of symmetry operations: 12

Parallelepiped containing an asymmetric unit:
  0<=x<1; 0<=y<=1/2; -1/12<=z<=1/12

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
-y,-x,-z+5/6 2[-1,1,0]0,0,00,0,5/12
x-y,-y,-z 2[1,0,0]0,0,00,0,0
x,x-y,-z+1/6 2[2,1,0]0,0,00,0,1/12
y,x,-z+1/3 2[1,1,0]0,0,00,0,1/6
-x+y,y,-z+1/2 2[1,2,0]0,0,00,0,1/4
-x,-x+y,-z+2/3 2[0,1,0]0,0,00,0,1/3 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
c121x,y,z
b62x,2*x,1/4
a62x,0,0 

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
x+y,x+y,2*z+5/6[-1,1,0]0,0,5/6
y,2*y,2*z[1,0,0]0,0,0
0,x-2*y,2*z+1/6[2,1,0]0,0,1/6
x+y,-x-y,2*z+1/3[1,1,0]0,0,1/3
2*x+y,0,2*z+1/2[1,2,0]0,0,1/2
2*x,x,2*z+2/3[0,1,0]0,0,2/3 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2

Grid factors implied by symmetries:
  Space group: (1, 1, 6)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (1, 1, 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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