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Result of symbol lookup:
  Space group number: 230
  Schoenflies symbol: Oh^10
  Hermann-Mauguin symbol: I a -3 d
  Hall symbol: -I 4bd 2c 3

Input space group symbol: I a -3 d
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<=1/8; -1/8<=y<=0; 1/8<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]0,0,1/4-1/4,1/2,0
-x+1/2,-y,z+1/2 2[0,0,1]0,0,1/21/4,0,0
y+1/4,-x+1/4,z+3/4 4^-1[0,0,1]0,0,3/41/4,0,0
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]1/2,1/2,0-1/4,0,3/8
-x+1/2,y,-z 2[0,1,0]0,0,01/4,0,0
-y+1/4,-x+1/4,-z+1/4 2[-1,1,0]0,0,01/4,0,1/8
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]0,1/2,1/21/8,1/4,0
-z+1/2,-x,y+1/2 3^-1[-1,1,1]0,0,01/2,-1/2,0
x+1/4,-z+1/4,y+3/4 4^1[1,0,0]1/4,0,00,-1/4,1/2
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]1/4,0,00,3/4,0
-z+1/2,x,-y 3^1[-1,-1,1]1/6,1/6,-1/61/3,1/6,0
-x+1/4,-z+1/4,-y+1/4 2[0,-1,1]0,0,01/8,1/4,0
y,z,x 3^-1[1,1,1]0,0,00,0,0
y+1/2,-z+1/2,-x 3^-1[-1,-1,1]1/3,1/3,-1/31/3,1/6,0
z+3/4,y+1/4,-x+1/4 4^1[0,1,0]0,1/4,01/2,0,-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+1/4,-y+1/4,-x+1/4 2[-1,0,1]0,0,01/4,1/8,0
-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+1/4 2[1,0,1]1/2,0,1/21/4,3/8,0
-z+3/4,y+1/4,x+3/4 4^-1[0,1,0]0,1/4,00,0,3/4
-x,-y,-z -1--0,0,0
y-1/4,-x-3/4,-z-1/4 -4^1[0,0,1]0,0,0-1/2,-1/4,-1/8
x-1/2,y,-z-1/2 -2[0,0,1]-1/2,0,00,0,-1/4
-y-1/4,x-1/4,-z-3/4 -4^-1[0,0,1]0,0,00,-1/4,-3/8
-x,y,z-1/2 -2[1,0,0]0,0,-1/20,0,0
-y-1/4,-x-3/4,z-3/4 -2[1,1,0]1/4,-1/4,-3/4-1/2,0,0
x-1/2,-y,z -2[0,1,0]-1/2,0,00,0,0
y-1/4,x-1/4,z-1/4 -2[-1,1,0]-1/4,-1/4,-1/40,0,0
-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-1/2,x,-y-1/2 -3^-1[-1,1,1]0,0,0-1/2,-1/2,0
-x-1/4,z-1/4,-y-3/4 -4^1[1,0,0]0,0,0-1/8,-1/2,-1/4
-z,x,y-1/2 -3^-1[1,-1,1]0,0,01/4,1/4,-1/4
-x-1/4,-z-3/4,y-3/4 -4^-1[1,0,0]0,0,0-1/8,0,-3/4
z-1/2,-x,y -3^1[-1,-1,1]0,0,0-1/4,1/4,1/4
x-1/4,z-1/4,y-1/4 -2[0,-1,1]-1/4,-1/4,-1/40,0,0
-y,-z,-x -3^-1[1,1,1]0,0,00,0,0
-y-1/2,z-1/2,x -3^-1[-1,-1,1]0,0,00,-1/2,0
-z-3/4,-y-1/4,x-1/4 -4^1[0,1,0]0,0,0-1/4,-1/8,-1/2
y,-z-1/2,x-1/2 -3^1[-1,1,1]0,0,00,0,-1/2
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]0,0,0-1/2,0,0
-z-3/4,y-3/4,-x-1/4 -2[1,0,1]-1/4,-3/4,1/4-1/2,0,0
z-3/4,-y-1/4,-x-3/4 -4^-1[0,1,0]0,0,0-3/4,-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]0,0,3/4-1/4,1,0
-x+1,-y+1/2,z+1 2[0,0,1]0,0,11/2,1/4,0
y+3/4,-x+3/4,z+5/4 4^-1[0,0,1]0,0,5/43/4,0,0
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]1,1,0-1/4,0,5/8
-x+1,y+1/2,-z+1/2 2[0,1,0]0,1/2,01/2,0,1/4
-y+3/4,-x+3/4,-z+3/4 2[-1,1,0]0,0,03/4,0,3/8
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]0,1,13/8,1/4,0
-z+1,-x+1/2,y+1 3^-1[-1,1,1]-1/6,1/6,1/67/6,-5/6,0
x+3/4,-z+3/4,y+5/4 4^1[1,0,0]3/4,0,00,-1/4,1
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]3/4,0,00,5/4,0
-z+1,x+1/2,-y+1/2 3^1[-1,-1,1]1/3,1/3,-1/32/3,5/6,0
-x+3/4,-z+3/4,-y+3/4 2[0,-1,1]0,0,03/8,3/4,0
y+1/2,z+1/2,x+1/2 3^-1[1,1,1]1/2,1/2,1/20,0,0
y+1,-z+1,-x+1/2 3^-1[-1,-1,1]1/2,1/2,-1/21,1/2,0
z+5/4,y+3/4,-x+3/4 4^1[0,1,0]0,3/4,01,0,-1/4
-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]0,0,03/4,3/8,0
-y+1,-z+1/2,x+1 3^1[1,-1,1]1/2,-1/2,1/2-1/2,1,0
z+5/4,-y+5/4,x+3/4 2[1,0,1]1,0,11/4,5/8,0
-z+5/4,y+3/4,x+5/4 4^-1[0,1,0]0,3/4,00,0,5/4
-x+1/2,-y+1/2,-z+1/2 -1--1/4,1/4,1/4
y+1/4,-x-1/4,-z+1/4 -4^1[0,0,1]0,0,00,-1/4,1/8
x,y+1/2,-z -2[0,0,1]0,1/2,00,0,0
-y+1/4,x+1/4,-z-1/4 -4^-1[0,0,1]0,0,00,1/4,-1/8
-x+1/2,y+1/2,z -2[1,0,0]0,1/2,01/4,0,0
-y+1/4,-x-1/4,z-1/4 -2[1,1,0]1/4,-1/4,-1/40,0,0
x,-y+1/2,z+1/2 -2[0,1,0]0,0,1/20,1/4,0
y+1/4,x+1/4,z+1/4 -2[-1,1,0]1/4,1/4,1/40,0,0
-z+1/2,-x+1/2,-y+1/2 -3^1[1,1,1]0,0,01/4,1/4,1/4
x+1/4,-z-1/4,-y+1/4 -2[0,1,1]1/4,-1/4,1/40,0,0
z,x+1/2,-y -3^-1[-1,1,1]0,0,0-1/4,1/4,-1/4
-x+1/4,z+1/4,-y-1/4 -4^1[1,0,0]0,0,01/8,0,-1/4
-z+1/2,x+1/2,y -3^-1[1,-1,1]0,0,00,1/2,1/2
-x+1/4,-z-1/4,y-1/4 -4^-1[1,0,0]0,0,01/8,0,-1/4
z,-x+1/2,y+1/2 -3^1[-1,-1,1]0,0,01/2,0,1/2
x+1/4,z+1/4,y+1/4 -2[0,-1,1]1/4,1/4,1/40,0,0
-y+1/2,-z+1/2,-x+1/2 -3^-1[1,1,1]0,0,01/4,1/4,1/4
-y,z,x+1/2 -3^-1[-1,-1,1]0,0,0-1/4,1/4,1/4
-z-1/4,-y+1/4,x+1/4 -4^1[0,1,0]0,0,0-1/4,1/8,0
y+1/2,-z,x -3^1[-1,1,1]0,0,01/4,-1/4,1/4
z+1/4,y+1/4,x+1/4 -2[-1,0,1]1/4,1/4,1/40,0,0
y,z+1/2,-x -3^1[1,-1,1]0,0,01/4,1/4,-1/4
-z-1/4,y-1/4,-x+1/4 -2[1,0,1]-1/4,-1/4,1/40,0,0
z-1/4,-y+1/4,-x-1/4 -4^-1[0,1,0]0,0,0-1/4,1/8,0 

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,0,1/4
e323x,x,x
d24-43/8,0,1/4
c242221/8,0,1/4
b16321/8,1/8,1/8
a16-30,0,0 

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

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