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Result of symbol lookup:
  Space group number: 139
  Schoenflies symbol: D4h^17
  Hermann-Mauguin symbol: I 4/m m m
  Hall symbol: -I 4 2

Input space group symbol: I 4/m m m
Convention: Default

Number of lattice translations: 2
Space group is centric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 32

Parallelepiped containing an asymmetric unit:
  0<=x<=1/2; 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
-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
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
-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 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
o321x,y,z
n16m0,y,z
m16mx,x,z
l16mx,y,0
k162x,x+1/2,1/4
j8mm2x,1/2,0
i8mm2x,0,0
h8mm2x,x,0
g8mm20,1/2,z
f82/m1/4,1/4,1/4
e44mm0,0,z
d4-42m0,1/2,1/4
c4mmm0,1/2,0
b24/mmm0,0,1/2
a24/mmm0,0,0 

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 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2

Grid factors implied by symmetries:
  Space group: (2, 2, 2)
  Structure-seminvariant vectors and moduli: (1, 1, 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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