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Result of symbol lookup:
  Space group number: 229
  Schoenflies symbol: Oh^9
  Hermann-Mauguin symbol: I m -3 m
  Hall symbol: -I 4 2 3

Input space group symbol: I m -3 m
Convention: Default

Number of lattice translations: 2
Space group is centric.
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<=1/2

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,-z -1--0,0,0
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]0,0,1/20,1/2,0
-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]0,0,1/21/2,0,0
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]1/2,1/2,00,0,1/4
-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]0,0,01/2,0,1/4
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]0,1/2,1/21/4,0,0
-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]1/2,0,00,0,1/2
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]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,-1/61/3,2/3,0
-x+1/2,-z+1/2,-y+1/2 2[0,-1,1]0,0,01/4,1/2,0
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]0,1/2,01/2,0,0
-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]0,0,01/2,1/4,0
-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]1/2,0,1/20,1/4,0
-z+1/2,y+1/2,x+1/2 4^-1[0,1,0]0,1/2,00,0,1/2
-x+1/2,-y+1/2,-z+1/2 -1--1/4,1/4,1/4
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]1/2,1/2,00,0,1/4
-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]0,1/2,1/21/4,0,0
-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]1/2,0,1/20,1/4,0
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]0,0,01/4,1/4,1/4
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]0,0,01/4,3/4,-1/4
-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]0,0,0-1/4,1/4,3/4
-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]0,0,03/4,-1/4,1/4
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]0,0,01/4,1/4,1/4
-y+1/2,z+1/2,x+1/2 -3^-1[-1,-1,1]0,0,0-1/4,3/4,1/4
-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]0,0,01/4,-1/4,3/4
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]0,0,03/4,1/4,-1/4
-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
l961x,y,z
k48mx,x,z
j48m0,y,z
i4821/4,y,-y+1/2
h24mm20,y,y
g24mm2x,0,1/2
f163mx,x,x
e124mmx,0,0
d12-42m1/4,0,1/2
c8-3m1/4,1/4,1/4
b64/mmm0,1/2,1/2
a2m-3m0,0,0 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 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.
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