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Result of symbol lookup:
  Space group number: 210
  Schoenflies symbol: O^4
  Hermann-Mauguin symbol: F 41 3 2
  Hall symbol: F 4d 2 3

Input space group symbol: F 41 3 2
Convention: Default

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

Parallelepiped containing an asymmetric unit:
  0<=x<=1/8; 0<=y<=1/8; 0<=z<1

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y+1/4,x+1/4,z+1/4 4^1[0,0,1]0,0,1/40,1/4,0
-x,-y+1/2,z+1/2 2[0,0,1]0,0,1/20,1/4,0
y+3/4,-x+1/4,z+3/4 4^-1[0,0,1]0,0,3/41/2,-1/4,0
x,-y,-z 2[1,0,0]0,0,00,0,0
y+1/4,x+1/4,-z+1/4 2[1,1,0]1/4,1/4,00,0,1/8
-x,y+1/2,-z+1/2 2[0,1,0]0,1/2,00,0,1/4
-y+3/4,-x+1/4,-z+3/4 2[-1,1,0]1/4,-1/4,01/2,0,3/8
z,x,y 3^1[1,1,1]0,0,00,0,0
-x+1/4,z+1/4,y+1/4 2[0,1,1]0,1/4,1/41/8,0,0
-z,-x+1/2,y+1/2 3^-1[-1,1,1]-1/3,1/3,1/31/3,-1/6,0
x+3/4,-z+1/4,y+3/4 4^1[1,0,0]3/4,0,00,-1/4,1/2
z,-x,-y 3^-1[1,-1,1]0,0,00,0,0
x+1/4,z+1/4,-y+1/4 4^-1[1,0,0]1/4,0,00,1/4,0
-z,x+1/2,-y+1/2 3^1[-1,-1,1]0,0,00,1/2,0
-x+3/4,-z+1/4,-y+3/4 2[0,-1,1]0,-1/4,1/43/8,1/2,0
y,z,x 3^-1[1,1,1]0,0,00,0,0
y+1/2,-z,-x+1/2 3^-1[-1,-1,1]0,0,01/2,0,0
z+1/4,y+3/4,-x+3/4 4^1[0,1,0]0,3/4,01/2,0,1/4
-y+1/2,z+1/2,-x 3^1[-1,1,1]0,0,00,1/2,0
-z+1/4,-y+1/4,-x+1/4 2[-1,0,1]0,0,01/4,1/8,0
-y,-z,x 3^1[1,-1,1]0,0,00,0,0
z+1/4,-y+3/4,x+3/4 2[1,0,1]1/2,0,1/2-1/4,3/8,0
-z+3/4,y+3/4,x+1/4 4^-1[0,1,0]0,3/4,01/4,0,1/2
x,y+1/2,z+1/2 1---
-y+1/4,x+3/4,z+3/4 4^1[0,0,1]0,0,3/4-1/4,1/2,0
-x,-y+1,z+1 2[0,0,1]0,0,10,1/2,0
y+3/4,-x+3/4,z+5/4 4^-1[0,0,1]0,0,5/43/4,0,0
x,-y+1/2,-z+1/2 2[1,0,0]0,0,00,1/4,1/4
y+1/4,x+3/4,-z+3/4 2[1,1,0]1/2,1/2,0-1/4,0,3/8
-x,y+1,-z+1 2[0,1,0]0,1,00,0,1/2
-y+3/4,-x+3/4,-z+5/4 2[-1,1,0]0,0,03/4,0,5/8
z,x+1/2,y+1/2 3^1[1,1,1]1/3,1/3,1/3-1/3,-1/6,0
-x+1/4,z+3/4,y+3/4 2[0,1,1]0,3/4,3/41/8,0,0
-z,-x+1,y+1 3^-1[-1,1,1]-2/3,2/3,2/32/3,-1/3,0
x+3/4,-z+3/4,y+5/4 4^1[1,0,0]3/4,0,00,-1/4,1
z,-x+1/2,-y+1/2 3^-1[1,-1,1]0,0,00,1/2,0
x+1/4,z+3/4,-y+3/4 4^-1[1,0,0]1/4,0,00,3/4,0
-z,x+1,-y+1 3^1[-1,-1,1]0,0,00,1,0
-x+3/4,-z+3/4,-y+5/4 2[0,-1,1]0,-1/4,1/43/8,1,0
y,z+1/2,x+1/2 3^-1[1,1,1]1/3,1/3,1/3-1/6,1/6,0
y+1/2,-z+1/2,-x+1 3^-1[-1,-1,1]0,0,01,1/2,0
z+1/4,y+5/4,-x+5/4 4^1[0,1,0]0,5/4,03/4,0,1/2
-y+1/2,z+1,-x+1/2 3^1[-1,1,1]-1/3,1/3,1/31/6,2/3,0
-z+1/4,-y+3/4,-x+3/4 2[-1,0,1]-1/4,0,1/41/2,3/8,0
-y,-z+1/2,x+1/2 3^1[1,-1,1]0,0,0-1/2,1/2,0
z+1/4,-y+5/4,x+5/4 2[1,0,1]3/4,0,3/4-1/2,5/8,0
-z+3/4,y+5/4,x+3/4 4^-1[0,1,0]0,5/4,00,0,3/4
x+1/2,y,z+1/2 1---
-y+3/4,x+1/4,z+3/4 4^1[0,0,1]0,0,3/41/4,1/2,0
-x+1/2,-y+1/2,z+1 2[0,0,1]0,0,11/4,1/4,0
y+5/4,-x+1/4,z+5/4 4^-1[0,0,1]0,0,5/43/4,-1/2,0
x+1/2,-y,-z+1/2 2[1,0,0]1/2,0,00,0,1/4
y+3/4,x+1/4,-z+3/4 2[1,1,0]1/2,1/2,01/4,0,3/8
-x+1/2,y+1/2,-z+1 2[0,1,0]0,1/2,01/4,0,1/2
-y+5/4,-x+1/4,-z+5/4 2[-1,1,0]1/2,-1/2,03/4,0,5/8
z+1/2,x,y+1/2 3^1[1,1,1]1/3,1/3,1/31/6,-1/6,0
-x+3/4,z+1/4,y+3/4 2[0,1,1]0,1/2,1/23/8,-1/4,0
-z+1/2,-x+1/2,y+1 3^-1[-1,1,1]-1/3,1/3,1/35/6,-2/3,0
x+5/4,-z+1/4,y+5/4 4^1[1,0,0]5/4,0,00,-1/2,3/4
z+1/2,-x,-y+1/2 3^-1[1,-1,1]1/3,-1/3,1/31/6,1/6,0
x+3/4,z+1/4,-y+3/4 4^-1[1,0,0]3/4,0,00,1/2,1/4
-z+1/2,x+1/2,-y+1 3^1[-1,-1,1]0,0,01/2,1,0
-x+5/4,-z+1/4,-y+5/4 2[0,-1,1]0,-1/2,1/25/8,3/4,0
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,-z,-x+1 3^-1[-1,-1,1]0,0,01,0,0
z+3/4,y+3/4,-x+5/4 4^1[0,1,0]0,3/4,01,0,1/4
-y+1,z+1/2,-x+1/2 3^1[-1,1,1]0,0,01/2,1/2,0
-z+3/4,-y+1/4,-x+3/4 2[-1,0,1]0,0,03/4,1/8,0
-y+1/2,-z,x+1/2 3^1[1,-1,1]1/3,-1/3,1/3-1/6,1/3,0
z+3/4,-y+3/4,x+5/4 2[1,0,1]1,0,1-1/4,3/8,0
-z+5/4,y+3/4,x+3/4 4^-1[0,1,0]0,3/4,01/4,0,1
x+1/2,y+1/2,z 1---
-y+3/4,x+3/4,z+1/4 4^1[0,0,1]0,0,1/40,3/4,0
-x+1/2,-y+1,z+1/2 2[0,0,1]0,0,1/21/4,1/2,0
y+5/4,-x+3/4,z+3/4 4^-1[0,0,1]0,0,3/41,-1/4,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
y+3/4,x+3/4,-z+1/4 2[1,1,0]3/4,3/4,00,0,1/8
-x+1/2,y+1,-z+1/2 2[0,1,0]0,1,01/4,0,1/4
-y+5/4,-x+3/4,-z+3/4 2[-1,1,0]1/4,-1/4,01,0,3/8
z+1/2,x+1/2,y 3^1[1,1,1]1/3,1/3,1/31/6,1/3,0
-x+3/4,z+3/4,y+1/4 2[0,1,1]0,1/2,1/23/8,1/4,0
-z+1/2,-x+1,y+1/2 3^-1[-1,1,1]-1/3,1/3,1/35/6,-1/6,0
x+5/4,-z+3/4,y+3/4 4^1[1,0,0]5/4,0,00,0,3/4
z+1/2,-x+1/2,-y 3^-1[1,-1,1]0,0,01/2,0,0
x+3/4,z+3/4,-y+1/4 4^-1[1,0,0]3/4,0,00,1/2,-1/4
-z+1/2,x+1,-y+1/2 3^1[-1,-1,1]1/3,1/3,-1/31/6,5/6,0
-x+5/4,-z+3/4,-y+3/4 2[0,-1,1]0,0,05/8,3/4,0
y+1/2,z+1/2,x 3^-1[1,1,1]1/3,1/3,1/31/3,1/6,0
y+1,-z+1/2,-x+1/2 3^-1[-1,-1,1]1/3,1/3,-1/35/6,1/6,0
z+3/4,y+5/4,-x+3/4 4^1[0,1,0]0,5/4,03/4,0,0
-y+1,z+1,-x 3^1[-1,1,1]0,0,00,1,0
-z+3/4,-y+3/4,-x+1/4 2[-1,0,1]1/4,0,-1/41/2,3/8,0
-y+1/2,-z+1/2,x 3^1[1,-1,1]0,0,00,1/2,0
z+3/4,-y+5/4,x+3/4 2[1,0,1]3/4,0,3/40,5/8,0
-z+5/4,y+5/4,x+1/4 4^-1[0,1,0]0,5/4,01/2,0,3/4 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
h961x,y,z
g4821/8,y,-y+1/4
f482x,0,0
e323x,x,x
d1632-3/8,-3/8,-3/8
c16321/8,1/8,1/8
b8231/2,1/2,1/2
a8230,0,0 

Harker planes:
Algebraic Normal vector A point in the plane
x-y+1/4,-x-y+1/4,1/4[0,0,1]1/4,1/4,1/4
2*x,2*y+1/2,1/2[0,0,1]0,1/2,1/2
0,2*y,2*z[1,0,0]0,0,0
x+y+1/4,-x-y+1/4,2*z+1/4[1,1,0]1/4,1/4,1/4
2*x,1/2,2*z+1/2[0,1,0]0,1/2,1/2
x+y+3/4,x+y+1/4,2*z+3/4[-1,1,0]3/4,1/4,3/4
x+z,-x-y,y-z[1,1,1]0,0,0
2*x+1/4,y+z+1/4,-y-z+1/4[0,1,1]1/4,1/4,1/4
3/4,y-z+1/4,-y-z+3/4[1,0,0]3/4,1/4,3/4
x+z,-x-y+1/2,-y+z+1/2[-1,-1,1]0,1/2,1/2
2*x+3/4,y+z+1/4,y+z+3/4[0,-1,1]3/4,1/4,3/4
x-z+1/4,3/4,x+z+3/4[0,1,0]1/4,3/4,3/4
x+y+1/2,y-z+1/2,x+z[-1,1,1]1/2,1/2,0
x+z+1/4,2*y+1/4,x+z+1/4[-1,0,1]1/4,1/4,1/4
x+y,y-z,-x-z[1,-1,1]0,0,0
x+z+1/4,2*y+3/4,-x-z+3/4[1,0,1]1/4,3/4,3/4 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 0, 0) 2
  Inversion through a centre at: 1/8,1/8,1/8

Grid factors implied by symmetries:
  Space group: (4, 4, 4)
  Structure-seminvariant vectors and moduli: (2, 1, 1)
  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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