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Result of symbol lookup:
  Space group number: 224
  Schoenflies symbol: Oh^4
  Hermann-Mauguin symbol: P n -3 m
  Origin choice: 2
  Hall symbol: -P 4bc 2bc 3

Input space group symbol: P n -3 m :2
Convention: Default

Number of lattice translations: 1
Space group is centric.
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+1/2,z+1/2 4^1[0,0,1]0,0,1/2-1/4,1/4,0
-x+1/2,-y+1/2,z 2[0,0,1]0,0,01/4,1/4,0
y+1/2,-x,z+1/2 4^-1[0,0,1]0,0,1/21/4,-1/4,0
x,-y+1/2,-z+1/2 2[1,0,0]0,0,00,1/4,1/4
y+1/2,x+1/2,-z 2[1,1,0]1/2,1/2,00,0,0
-x+1/2,y,-z+1/2 2[0,1,0]0,0,01/4,0,1/4
-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+1/2,y+1/2 2[0,1,1]0,1/2,1/20,0,0
-z+1/2,-x+1/2,y 3^-1[-1,1,1]0,0,01/2,0,0
x+1/2,-z,y+1/2 4^1[1,0,0]1/2,0,00,-1/4,1/4
z,-x+1/2,-y+1/2 3^-1[1,-1,1]0,0,00,1/2,0
x+1/2,z+1/2,-y 4^-1[1,0,0]1/2,0,00,1/4,-1/4
-z+1/2,x,-y+1/2 3^1[-1,-1,1]0,0,01/2,1/2,0
-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+1/2,-x+1/2 3^-1[-1,-1,1]0,0,01/2,1/2,0
z+1/2,y+1/2,-x 4^1[0,1,0]0,1/2,01/4,0,-1/4
-y+1/2,z,-x+1/2 3^1[-1,1,1]0,0,01/2,0,0
-z,-y,-x 2[-1,0,1]0,0,00,0,0
-y+1/2,-z+1/2,x 3^1[1,-1,1]0,0,00,1/2,0
z+1/2,-y,x+1/2 2[1,0,1]1/2,0,1/20,0,0
-z,y+1/2,x+1/2 4^-1[0,1,0]0,1/2,0-1/4,0,1/4
-x,-y,-z -1--0,0,0
y,-x-1/2,-z-1/2 -4^1[0,0,1]0,0,0-1/4,-1/4,-1/4
x-1/2,y-1/2,-z -2[0,0,1]-1/2,-1/2,00,0,0
-y-1/2,x,-z-1/2 -4^-1[0,0,1]0,0,0-1/4,-1/4,-1/4
-x,y-1/2,z-1/2 -2[1,0,0]0,-1/2,-1/20,0,0
-y-1/2,-x-1/2,z -2[1,1,0]0,0,0-1/2,0,0
x-1/2,-y,z-1/2 -2[0,1,0]-1/2,0,-1/20,0,0
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-1/2,-y-1/2 -2[0,1,1]0,0,00,-1/2,0
z-1/2,x-1/2,-y -3^-1[-1,1,1]0,0,00,-1/2,1/2
-x-1/2,z,-y-1/2 -4^1[1,0,0]0,0,0-1/4,-1/4,-1/4
-z,x-1/2,y-1/2 -3^-1[1,-1,1]0,0,01/2,0,-1/2
-x-1/2,-z-1/2,y -4^-1[1,0,0]0,0,0-1/4,-1/4,-1/4
z-1/2,-x,y-1/2 -3^1[-1,-1,1]0,0,0-1/2,1/2,0
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-1/2,x-1/2 -3^-1[-1,-1,1]0,0,01/2,-1/2,0
-z-1/2,-y-1/2,x -4^1[0,1,0]0,0,0-1/4,-1/4,-1/4
y-1/2,-z,x-1/2 -3^1[-1,1,1]0,0,00,1/2,-1/2
z,y,x -2[-1,0,1]0,0,00,0,0
y-1/2,z-1/2,-x -3^1[1,-1,1]0,0,0-1/2,0,1/2
-z-1/2,y,-x-1/2 -2[1,0,1]0,0,0-1/2,0,0
z,-y-1/2,-x-1/2 -4^-1[0,1,0]0,0,0-1/4,-1/4,-1/4 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
l481x,y,z
k24mx,x,z
j2421/2,y,y+1/2
i2421/2,y,-y
h242x,1/4,-1/4
g12mm2x,1/4,1/4
f122221/2,1/4,-1/4
e83mx,x,x
d6-42m1/4,-1/4,-1/4
c4-3m1/2,1/2,1/2
b4-3m0,0,0
a2-43m1/4,1/4,1/4 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 1, 1) 2

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