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Result of symbol lookup:
  Space group number: 105
  Schoenflies symbol: C4v^7
  Hermann-Mauguin symbol: P 42 m c
  Hall symbol: P 4c -2

Input space group symbol: P 42 m 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<=1/2; 0<=y<=1/2; 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,y,z -2[1,0,0]0,0,00,0,0
-y,-x,z+1/2 -2[1,1,0]0,0,1/20,0,0
x,-y,z -2[0,1,0]0,0,00,0,0
y,x,z+1/2 -2[-1,1,0]0,0,1/20,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
f81x,y,z
e4mx,1/2,z
d4mx,0,z
c2mm20,1/2,z
b2mm21/2,1/2,z
a2mm20,0,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: (1, 1, 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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