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Result of symbol lookup:
  Space group number: 182
  Schoenflies symbol: D6^6
  Hermann-Mauguin symbol: P 63 2 2
  Hall symbol: P 6c 2c

Input space group symbol: P 63 2 2
Convention: Default

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

Parallelepiped containing an asymmetric unit:
  0<=x<=2/3; 0<=y<=1/3; 1/4<=z<=3/4

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

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
i121x,y,z
h62x,2*x,1/4
g62x,0,0
f431/3,-1/3,z
e430,0,z
d2321/3,-1/3,-1/4
c2321/3,-1/3,1/4
b2320,0,1/4
a2320,0,0 

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

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

Grid factors implied by symmetries:
  Space group: (1, 1, 2)
  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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