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Result of symbol lookup:
  Space group number: 141
  Schoenflies symbol: D4h^19
  Hermann-Mauguin symbol: I 41/a m d
  Origin choice: 2
  Hall symbol: -I 4bd 2

Input space group symbol: I 41/a m d :2
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<=1/4; 0<=y<=1/4; -1/8<=z<=3/8

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 2[1,0,0]0,0,00,0,0
y+1/4,x+3/4,-z+1/4 2[1,1,0]1/2,1/2,0-1/4,0,1/8
-x+1/2,y,-z+1/2 2[0,1,0]0,0,01/4,0,1/4
-y+1/4,-x+1/4,-z+3/4 2[-1,1,0]0,0,01/4,0,3/8
-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 -2[1,0,0]0,0,00,0,0
-y-1/4,-x-3/4,z-1/4 -2[1,1,0]1/4,-1/4,-1/4-1/2,0,0
x-1/2,-y,z-1/2 -2[0,1,0]-1/2,0,-1/20,0,0
y-1/4,x-1/4,z-3/4 -2[-1,1,0]-1/4,-1/4,-3/40,0,0
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 2[1,0,0]1/2,0,00,1/4,1/4
y+3/4,x+5/4,-z+3/4 2[1,1,0]1,1,0-1/4,0,3/8
-x+1,y+1/2,-z+1 2[0,1,0]0,1/2,01/2,0,1/2
-y+3/4,-x+3/4,-z+5/4 2[-1,1,0]0,0,03/4,0,5/8
-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+1/2 -2[1,0,0]0,1/2,1/21/4,0,0
-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 -2[0,1,0]0,0,00,1/4,0
y+1/4,x+1/4,z-1/4 -2[-1,1,0]1/4,1/4,-1/40,0,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
i321x,y,z
h16m0,y,z
g162x,x+1/4,-1/8
f162x,0,0
e8mm20,1/4,z
d82/m0,0,1/2
c82/m0,0,0
b4-42m0,1/4,3/8
a4-42m0,-1/4,1/8 

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[1,0,0]0,0,0
x+y+1/4,-x-y+3/4,2*z+1/4[1,1,0]1/4,3/4,1/4
2*x+1/2,0,2*z+1/2[0,1,0]1/2,0,1/2
x+y+1/4,x+y+1/4,2*z+3/4[-1,1,0]1/4,1/4,3/4 

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: (4, 4, 4)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  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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