[Index of services] [New input] 
Result of symbol lookup:
  Space group number: 217
  Schoenflies symbol: Td^3
  Hermann-Mauguin symbol: I -4 3 m
  Hall symbol: I -4 2 3

Input space group symbol: I -4 3 m
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:
  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+1/2,y+1/2,z+1/2 1---
y+1/2,-x+1/2,-z+1/2 -4^1[0,0,1]0,0,01/2,0,1/4
-x+1/2,-y+1/2,z+1/2 2[0,0,1]0,0,1/21/4,1/4,0
-y+1/2,x+1/2,-z+1/2 -4^-1[0,0,1]0,0,00,1/2,1/4
x+1/2,-y+1/2,-z+1/2 2[1,0,0]1/2,0,00,1/4,1/4
-y+1/2,-x+1/2,z+1/2 -2[1,1,0]0,0,1/21/2,0,0
-x+1/2,y+1/2,-z+1/2 2[0,1,0]0,1/2,01/4,0,1/4
y+1/2,x+1/2,z+1/2 -2[-1,1,0]1/2,1/2,1/20,0,0
z+1/2,x+1/2,y+1/2 3^1[1,1,1]1/2,1/2,1/20,0,0
x+1/2,-z+1/2,-y+1/2 -2[0,1,1]1/2,0,00,1/2,0
-z+1/2,-x+1/2,y+1/2 3^-1[-1,1,1]-1/6,1/6,1/62/3,-1/3,0
-x+1/2,z+1/2,-y+1/2 -4^1[1,0,0]0,0,01/4,1/2,0
z+1/2,-x+1/2,-y+1/2 3^-1[1,-1,1]1/6,-1/6,1/61/3,1/3,0
-x+1/2,-z+1/2,y+1/2 -4^-1[1,0,0]0,0,01/4,0,1/2
-z+1/2,x+1/2,-y+1/2 3^1[-1,-1,1]1/6,1/6,-1/61/3,2/3,0
x+1/2,z+1/2,y+1/2 -2[0,-1,1]1/2,1/2,1/20,0,0
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+1/2 3^-1[-1,-1,1]1/6,1/6,-1/62/3,1/3,0
-z+1/2,-y+1/2,x+1/2 -4^1[0,1,0]0,0,00,1/4,1/2
-y+1/2,z+1/2,-x+1/2 3^1[-1,1,1]-1/6,1/6,1/61/3,1/3,0
z+1/2,y+1/2,x+1/2 -2[-1,0,1]1/2,1/2,1/20,0,0
-y+1/2,-z+1/2,x+1/2 3^1[1,-1,1]1/6,-1/6,1/6-1/3,2/3,0
-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
h481x,y,z
g24mx,x,z
f242x,1/2,0
e12mm2x,0,0
d12-41/4,1/2,0
c83mx,x,x
b6-42m0,1/2,1/2
a2-43m0,0,0 

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

Grid factors implied by symmetries:
  Space group: (2, 2, 2)
  Structure-seminvariant vectors and moduli: (1, 1, 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.
[Index of services] [New input]