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Result of symbol lookup:
  Space group number: 106
  Schoenflies symbol: C4v^8
  Hermann-Mauguin symbol: P 42 b c
  Hall symbol: P 4c -2ab

Input space group symbol: P 42 b c
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 8

Parallelepiped containing an asymmetric unit:
  0<=x<1; 0<=y<=1/4; 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,z+1/2 4^1[0,0,1]0,0,1/20,0,0
-x,-y,z 2[0,0,1]0,0,00,0,0
y,-x,z+1/2 4^-1[0,0,1]0,0,1/20,0,0
-x+1/2,y+1/2,z -2[1,0,0]0,1/2,01/4,0,0
-y+1/2,-x+1/2,z+1/2 -2[1,1,0]0,0,1/21/2,0,0
x+1/2,-y+1/2,z -2[0,1,0]1/2,0,00,1/4,0
y+1/2,x+1/2,z+1/2 -2[-1,1,0]1/2,1/2,1/20,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
c81x,y,z
b420,1/2,z
a420,0,z

Harker planes:
Algebraic Normal vector A point in the plane
x-y,-x-y,1/2[0,0,1]0,0,1/2
2*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, 1, 0) 2
  Inversion through a centre at: 0,0,0

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