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Result of symbol lookup:
  Space group number: 218
  Schoenflies symbol: Td^4
  Hermann-Mauguin symbol: P -4 3 n
  Hall symbol: P -4n 2 3

Input space group symbol: P -4 3 n
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 24
Total number of symmetry operations: 24

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

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
y+1/2,-x+1/2,-z+1/2 -4^1[0,0,1]0,0,01/2,0,1/4
-x,-y,z 2[0,0,1]0,0,00,0,0
-y+1/2,x+1/2,-z+1/2 -4^-1[0,0,1]0,0,00,1/2,1/4
x,-y,-z 2[1,0,0]0,0,00,0,0
-y+1/2,-x+1/2,z+1/2 -2[1,1,0]0,0,1/21/2,0,0
-x,y,-z 2[0,1,0]0,0,00,0,0
y+1/2,x+1/2,z+1/2 -2[-1,1,0]1/2,1/2,1/20,0,0
z,x,y 3^1[1,1,1]0,0,00,0,0
x+1/2,-z+1/2,-y+1/2 -2[0,1,1]1/2,0,00,1/2,0
-z,-x,y 3^-1[-1,1,1]0,0,00,0,0
-x+1/2,z+1/2,-y+1/2 -4^1[1,0,0]0,0,01/4,1/2,0
z,-x,-y 3^-1[1,-1,1]0,0,00,0,0
-x+1/2,-z+1/2,y+1/2 -4^-1[1,0,0]0,0,01/4,0,1/2
-z,x,-y 3^1[-1,-1,1]0,0,00,0,0
x+1/2,z+1/2,y+1/2 -2[0,-1,1]1/2,1/2,1/20,0,0
y,z,x 3^-1[1,1,1]0,0,00,0,0
y,-z,-x 3^-1[-1,-1,1]0,0,00,0,0
-z+1/2,-y+1/2,x+1/2 -4^1[0,1,0]0,0,00,1/4,1/2
-y,z,-x 3^1[-1,1,1]0,0,00,0,0
z+1/2,y+1/2,x+1/2 -2[-1,0,1]1/2,1/2,1/20,0,0
-y,-z,x 3^1[1,-1,1]0,0,00,0,0
-z+1/2,y+1/2,-x+1/2 -2[1,0,1]0,1/2,01/2,0,0
z+1/2,-y+1/2,-x+1/2 -4^-1[0,1,0]0,0,01/2,1/4,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
i241x,y,z
h122x,0,1/2
g122x,1/2,0
f122x,0,0
e83x,x,x
d6-41/4,0,1/2
c6-41/4,1/2,0
b62220,1/2,1/2
a2230,0,0 

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

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