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Result of symbol lookup:
  Space group number: 220
  Schoenflies symbol: Td^6
  Hermann-Mauguin symbol: I -4 3 d
  Hall symbol: I -4bd 2c 3

Input space group symbol: I -4 3 d
Convention: Default

Number of lattice translations: 2
Space group is acentric.
Number of representative symmetry operations: 24
Total number of symmetry operations: 48

Parallelepiped containing an asymmetric unit:
  -1/8<=x<=1/8; 0<=y<=1/8; 0<z<7/8

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
y+1/4,-x+3/4,-z+1/4 -4^1[0,0,1]0,0,01/2,1/4,1/8
-x,-y+1/2,z 2[0,0,1]0,0,00,1/4,0
-y+3/4,x+3/4,-z+1/4 -4^-1[0,0,1]0,0,00,3/4,1/8
x,-y,-z+1/2 2[1,0,0]0,0,00,0,1/4
-y+1/4,-x+3/4,z+3/4 -2[1,1,0]-1/4,1/4,3/41/2,0,0
-x,y+1/2,-z+1/2 2[0,1,0]0,1/2,00,0,1/4
y+3/4,x+3/4,z+3/4 -2[-1,1,0]3/4,3/4,3/40,0,0
z,x,y 3^1[1,1,1]0,0,00,0,0
x+1/4,-z+3/4,-y+1/4 -2[0,1,1]1/4,1/4,-1/40,1/2,0
-z,-x+1/2,y 3^-1[-1,1,1]-1/6,1/6,1/61/6,1/6,0
-x+3/4,z+3/4,-y+1/4 -4^1[1,0,0]0,0,03/8,1/2,-1/4
z,-x,-y+1/2 3^-1[1,-1,1]1/6,-1/6,1/6-1/6,1/3,0
-x+1/4,-z+3/4,y+3/4 -4^-1[1,0,0]0,0,01/8,0,3/4
-z,x+1/2,-y+1/2 3^1[-1,-1,1]0,0,00,1/2,0
x+3/4,z+3/4,y+3/4 -2[0,-1,1]3/4,3/4,3/40,0,0
y,z,x 3^-1[1,1,1]0,0,00,0,0
y,-z,-x+1/2 3^-1[-1,-1,1]-1/6,-1/6,1/61/3,1/6,0
-z+1/4,-y+3/4,x+3/4 -4^1[0,1,0]0,0,0-1/4,3/8,1/2
-y,z+1/2,-x+1/2 3^1[-1,1,1]-1/3,1/3,1/31/6,1/6,0
z+1/4,y+1/4,x+1/4 -2[-1,0,1]1/4,1/4,1/40,0,0
-y+1/2,-z,x+1/2 3^1[1,-1,1]1/3,-1/3,1/3-1/6,1/3,0
-z+1/4,y+1/4,-x+3/4 -2[1,0,1]-1/4,1/4,1/41/2,0,0
z+3/4,-y+1/4,-x+3/4 -4^-1[0,1,0]0,0,03/4,1/8,0
x+1/2,y+1/2,z+1/2 1---
y+3/4,-x+5/4,-z+3/4 -4^1[0,0,1]0,0,01,1/4,3/8
-x+1/2,-y+1,z+1/2 2[0,0,1]0,0,1/21/4,1/2,0
-y+5/4,x+5/4,-z+3/4 -4^-1[0,0,1]0,0,00,5/4,3/8
x+1/2,-y+1/2,-z+1 2[1,0,0]1/2,0,00,1/4,1/2
-y+3/4,-x+5/4,z+5/4 -2[1,1,0]-1/4,1/4,5/41,0,0
-x+1/2,y+1,-z+1 2[0,1,0]0,1,01/4,0,1/2
y+5/4,x+5/4,z+5/4 -2[-1,1,0]5/4,5/4,5/40,0,0
z+1/2,x+1/2,y+1/2 3^1[1,1,1]1/2,1/2,1/20,0,0
x+3/4,-z+5/4,-y+3/4 -2[0,1,1]3/4,1/4,-1/40,1,0
-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+5/4,-y+3/4 -4^1[1,0,0]0,0,05/8,1,-1/4
z+1/2,-x+1/2,-y+1 3^-1[1,-1,1]1/3,-1/3,1/31/6,2/3,0
-x+3/4,-z+5/4,y+5/4 -4^-1[1,0,0]0,0,03/8,0,5/4
-z+1/2,x+1,-y+1 3^1[-1,-1,1]1/6,1/6,-1/61/3,7/6,0
x+5/4,z+5/4,y+5/4 -2[0,-1,1]5/4,5/4,5/40,0,0
y+1/2,z+1/2,x+1/2 3^-1[1,1,1]1/2,1/2,1/20,0,0
y+1/2,-z+1/2,-x+1 3^-1[-1,-1,1]0,0,01,1/2,0
-z+3/4,-y+5/4,x+5/4 -4^1[0,1,0]0,0,0-1/4,5/8,1
-y+1/2,z+1,-x+1 3^1[-1,1,1]-1/2,1/2,1/21/2,1/2,0
z+3/4,y+3/4,x+3/4 -2[-1,0,1]3/4,3/4,3/40,0,0
-y+1,-z+1/2,x+1 3^1[1,-1,1]1/2,-1/2,1/2-1/2,1,0
-z+3/4,y+3/4,-x+5/4 -2[1,0,1]-1/4,3/4,1/41,0,0
z+5/4,-y+3/4,-x+5/4 -4^-1[0,1,0]0,0,05/4,3/8,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
e481x,y,z
d242x,0,1/4
c163x,x,x
b12-4-1/8,0,1/4
a12-43/8,0,1/4 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 0
  Inversion through a centre at: 0,0,0

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