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Result of symbol lookup:
  Space group number: 216
  Schoenflies symbol: Td^2
  Hermann-Mauguin symbol: F -4 3 m
  Hall symbol: F -4 2 3

Input space group symbol: F -4 3 m
Convention: Default

Number of lattice translations: 4
Space group is acentric.
Number of representative symmetry operations: 24
Total number of symmetry operations: 96

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,-x,-z -4^1[0,0,1]0,0,00,0,0
-x,-y,z 2[0,0,1]0,0,00,0,0
-y,x,-z -4^-1[0,0,1]0,0,00,0,0
x,-y,-z 2[1,0,0]0,0,00,0,0
-y,-x,z -2[1,1,0]0,0,00,0,0
-x,y,-z 2[0,1,0]0,0,00,0,0
y,x,z -2[-1,1,0]0,0,00,0,0
z,x,y 3^1[1,1,1]0,0,00,0,0
x,-z,-y -2[0,1,1]0,0,00,0,0
-z,-x,y 3^-1[-1,1,1]0,0,00,0,0
-x,z,-y -4^1[1,0,0]0,0,00,0,0
z,-x,-y 3^-1[1,-1,1]0,0,00,0,0
-x,-z,y -4^-1[1,0,0]0,0,00,0,0
-z,x,-y 3^1[-1,-1,1]0,0,00,0,0
x,z,y -2[0,-1,1]0,0,00,0,0
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,-y,x -4^1[0,1,0]0,0,00,0,0
-y,z,-x 3^1[-1,1,1]0,0,00,0,0
z,y,x -2[-1,0,1]0,0,00,0,0
-y,-z,x 3^1[1,-1,1]0,0,00,0,0
-z,y,-x -2[1,0,1]0,0,00,0,0
z,-y,-x -4^-1[0,1,0]0,0,00,0,0
x,y+1/2,z+1/2 1---
y,-x+1/2,-z+1/2 -4^1[0,0,1]0,0,01/4,1/4,1/4
-x,-y+1/2,z+1/2 2[0,0,1]0,0,1/20,1/4,0
-y,x+1/2,-z+1/2 -4^-1[0,0,1]0,0,0-1/4,1/4,1/4
x,-y+1/2,-z+1/2 2[1,0,0]0,0,00,1/4,1/4
-y,-x+1/2,z+1/2 -2[1,1,0]-1/4,1/4,1/21/4,0,0
-x,y+1/2,-z+1/2 2[0,1,0]0,1/2,00,0,1/4
y,x+1/2,z+1/2 -2[-1,1,0]1/4,1/4,1/2-1/4,0,0
z,x+1/2,y+1/2 3^1[1,1,1]1/3,1/3,1/3-1/3,-1/6,0
x,-z+1/2,-y+1/2 -2[0,1,1]0,0,00,1/2,0
-z,-x+1/2,y+1/2 3^-1[-1,1,1]-1/3,1/3,1/31/3,-1/6,0
-x,z+1/2,-y+1/2 -4^1[1,0,0]0,0,00,1/2,0
z,-x+1/2,-y+1/2 3^-1[1,-1,1]0,0,00,1/2,0
-x,-z+1/2,y+1/2 -4^-1[1,0,0]0,0,00,0,1/2
-z,x+1/2,-y+1/2 3^1[-1,-1,1]0,0,00,1/2,0
x,z+1/2,y+1/2 -2[0,-1,1]0,1/2,1/20,0,0
y,z+1/2,x+1/2 3^-1[1,1,1]1/3,1/3,1/3-1/6,1/6,0
y,-z+1/2,-x+1/2 3^-1[-1,-1,1]0,0,01/2,1/2,0
-z,-y+1/2,x+1/2 -4^1[0,1,0]0,0,0-1/4,1/4,1/4
-y,z+1/2,-x+1/2 3^1[-1,1,1]-1/3,1/3,1/31/6,1/6,0
z,y+1/2,x+1/2 -2[-1,0,1]1/4,1/2,1/4-1/4,0,0
-y,-z+1/2,x+1/2 3^1[1,-1,1]0,0,0-1/2,1/2,0
-z,y+1/2,-x+1/2 -2[1,0,1]-1/4,1/2,1/41/4,0,0
z,-y+1/2,-x+1/2 -4^-1[0,1,0]0,0,01/4,1/4,1/4
x+1/2,y,z+1/2 1---
y+1/2,-x,-z+1/2 -4^1[0,0,1]0,0,01/4,-1/4,1/4
-x+1/2,-y,z+1/2 2[0,0,1]0,0,1/21/4,0,0
-y+1/2,x,-z+1/2 -4^-1[0,0,1]0,0,01/4,1/4,1/4
x+1/2,-y,-z+1/2 2[1,0,0]1/2,0,00,0,1/4
-y+1/2,-x,z+1/2 -2[1,1,0]1/4,-1/4,1/21/4,0,0
-x+1/2,y,-z+1/2 2[0,1,0]0,0,01/4,0,1/4
y+1/2,x,z+1/2 -2[-1,1,0]1/4,1/4,1/21/4,0,0
z+1/2,x,y+1/2 3^1[1,1,1]1/3,1/3,1/31/6,-1/6,0
x+1/2,-z,-y+1/2 -2[0,1,1]1/2,-1/4,1/40,1/4,0
-z+1/2,-x,y+1/2 3^-1[-1,1,1]0,0,01/2,-1/2,0
-x+1/2,z,-y+1/2 -4^1[1,0,0]0,0,01/4,1/4,1/4
z+1/2,-x,-y+1/2 3^-1[1,-1,1]1/3,-1/3,1/31/6,1/6,0
-x+1/2,-z,y+1/2 -4^-1[1,0,0]0,0,01/4,-1/4,1/4
-z+1/2,x,-y+1/2 3^1[-1,-1,1]0,0,01/2,1/2,0
x+1/2,z,y+1/2 -2[0,-1,1]1/2,1/4,1/40,-1/4,0
y+1/2,z,x+1/2 3^-1[1,1,1]1/3,1/3,1/3-1/6,-1/3,0
y+1/2,-z,-x+1/2 3^-1[-1,-1,1]0,0,01/2,0,0
-z+1/2,-y,x+1/2 -4^1[0,1,0]0,0,00,0,1/2
-y+1/2,z,-x+1/2 3^1[-1,1,1]0,0,01/2,0,0
z+1/2,y,x+1/2 -2[-1,0,1]1/2,0,1/20,0,0
-y+1/2,-z,x+1/2 3^1[1,-1,1]1/3,-1/3,1/3-1/6,1/3,0
-z+1/2,y,-x+1/2 -2[1,0,1]0,0,01/2,0,0
z+1/2,-y,-x+1/2 -4^-1[0,1,0]0,0,01/2,0,0
x+1/2,y+1/2,z 1---
y+1/2,-x+1/2,-z -4^1[0,0,1]0,0,01/2,0,0
-x+1/2,-y+1/2,z 2[0,0,1]0,0,01/4,1/4,0
-y+1/2,x+1/2,-z -4^-1[0,0,1]0,0,00,1/2,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
-y+1/2,-x+1/2,z -2[1,1,0]0,0,01/2,0,0
-x+1/2,y+1/2,-z 2[0,1,0]0,1/2,01/4,0,0
y+1/2,x+1/2,z -2[-1,1,0]1/2,1/2,00,0,0
z+1/2,x+1/2,y 3^1[1,1,1]1/3,1/3,1/31/6,1/3,0
x+1/2,-z+1/2,-y -2[0,1,1]1/2,1/4,-1/40,1/4,0
-z+1/2,-x+1/2,y 3^-1[-1,1,1]0,0,01/2,0,0
-x+1/2,z+1/2,-y -4^1[1,0,0]0,0,01/4,1/4,-1/4
z+1/2,-x+1/2,-y 3^-1[1,-1,1]0,0,01/2,0,0
-x+1/2,-z+1/2,y -4^-1[1,0,0]0,0,01/4,1/4,1/4
-z+1/2,x+1/2,-y 3^1[-1,-1,1]1/3,1/3,-1/31/6,1/3,0
x+1/2,z+1/2,y -2[0,-1,1]1/2,1/4,1/40,1/4,0
y+1/2,z+1/2,x 3^-1[1,1,1]1/3,1/3,1/31/3,1/6,0
y+1/2,-z+1/2,-x 3^-1[-1,-1,1]1/3,1/3,-1/31/3,1/6,0
-z+1/2,-y+1/2,x -4^1[0,1,0]0,0,01/4,1/4,1/4
-y+1/2,z+1/2,-x 3^1[-1,1,1]0,0,00,1/2,0
z+1/2,y+1/2,x -2[-1,0,1]1/4,1/2,1/41/4,0,0
-y+1/2,-z+1/2,x 3^1[1,-1,1]0,0,00,1/2,0
-z+1/2,y+1/2,-x -2[1,0,1]1/4,1/2,-1/41/4,0,0
z+1/2,-y+1/2,-x -4^-1[0,1,0]0,0,01/4,1/4,-1/4 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
i961x,y,z
h48mx,x,z
g24mm2x,1/4,1/4
f24mm2x,0,0
e163mx,x,x
d4-43m-1/4,-1/4,-1/4
c4-43m1/4,1/4,1/4
b4-43m1/2,1/2,1/2
a4-43m0,0,0 

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) 4
  Inversion through a centre at: 0,0,0

Grid factors implied by symmetries:
  Space group: (2, 2, 2)
  Structure-seminvariant vectors and moduli: (4, 4, 4)
  Euclidean normalizer: (4, 4, 4)

  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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