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Input space group symbol: -F 4ud 2ud
Convention: Hall symbol

Number of lattice translations: 4
Space group is centric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 64

Parallelepiped containing an asymmetric unit:
  cctbx Error: Brick is not available for the given space group representation.

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y+1/2,x+1/4,z+1/4 4^1[0,0,1]0,0,1/41/8,3/8,0
-x+1/4,-y+3/4,z+1/2 2[0,0,1]0,0,1/21/8,3/8,0
y+3/4,-x+1/2,z+3/4 4^-1[0,0,1]0,0,3/45/8,-1/8,0
x+1/2,-y+1/4,-z+1/4 2[1,0,0]1/2,0,00,1/8,1/8
y+1/4,x+3/4,-z+1/2 2[1,1,0]1/2,1/2,0-1/4,0,1/4
-x+3/4,y+1/2,-z+3/4 2[0,1,0]0,1/2,03/8,0,3/8
-y,-x,-z 2[-1,1,0]0,0,00,0,0
-x,-y,-z -1--0,0,0
y-1/2,-x-1/4,-z-1/4 -4^1[0,0,1]0,0,0-3/8,1/8,-1/8
x-1/4,y-3/4,-z-1/2 -2[0,0,1]-1/4,-3/4,00,0,-1/4
-y-3/4,x-1/2,-z-3/4 -4^-1[0,0,1]0,0,0-1/8,-5/8,-3/8
-x-1/2,y-1/4,z-1/4 -2[1,0,0]0,-1/4,-1/4-1/4,0,0
-y-1/4,-x-3/4,z-1/2 -2[1,1,0]1/4,-1/4,-1/2-1/2,0,0
x-3/4,-y-1/2,z-3/4 -2[0,1,0]-3/4,0,-3/40,-1/4,0
y,x,z -2[-1,1,0]0,0,00,0,0
x,y+1/2,z+1/2 1---
-y+1/2,x+3/4,z+3/4 4^1[0,0,1]0,0,3/4-1/8,5/8,0
-x+1/4,-y+5/4,z+1 2[0,0,1]0,0,11/8,5/8,0
y+3/4,-x+1,z+5/4 4^-1[0,0,1]0,0,5/47/8,1/8,0
x+1/2,-y+3/4,-z+3/4 2[1,0,0]1/2,0,00,3/8,3/8
y+1/4,x+5/4,-z+1 2[1,1,0]3/4,3/4,0-1/2,0,1/2
-x+3/4,y+1,-z+5/4 2[0,1,0]0,1,03/8,0,5/8
-y,-x+1/2,-z+1/2 2[-1,1,0]-1/4,1/4,01/4,0,1/4
-x,-y+1/2,-z+1/2 -1--0,1/4,1/4
y-1/2,-x+1/4,-z+1/4 -4^1[0,0,1]0,0,0-1/8,3/8,1/8
x-1/4,y-1/4,-z -2[0,0,1]-1/4,-1/4,00,0,0
-y-3/4,x,-z-1/4 -4^-1[0,0,1]0,0,0-3/8,-3/8,-1/8
-x-1/2,y+1/4,z+1/4 -2[1,0,0]0,1/4,1/4-1/4,0,0
-y-1/4,-x-1/4,z -2[1,1,0]0,0,0-1/4,0,0
x-3/4,-y,z-1/4 -2[0,1,0]-3/4,0,-1/40,0,0
y,x+1/2,z+1/2 -2[-1,1,0]1/4,1/4,1/2-1/4,0,0
x+1/2,y,z+1/2 1---
-y+1,x+1/4,z+3/4 4^1[0,0,1]0,0,3/43/8,5/8,0
-x+3/4,-y+3/4,z+1 2[0,0,1]0,0,13/8,3/8,0
y+5/4,-x+1/2,z+5/4 4^-1[0,0,1]0,0,5/47/8,-3/8,0
x+1,-y+1/4,-z+3/4 2[1,0,0]1,0,00,1/8,3/8
y+3/4,x+3/4,-z+1 2[1,1,0]3/4,3/4,00,0,1/2
-x+5/4,y+1/2,-z+5/4 2[0,1,0]0,1/2,05/8,0,5/8
-y+1/2,-x,-z+1/2 2[-1,1,0]1/4,-1/4,01/4,0,1/4
-x+1/2,-y,-z+1/2 -1--1/4,0,1/4
y,-x-1/4,-z+1/4 -4^1[0,0,1]0,0,0-1/8,-1/8,1/8
x+1/4,y-3/4,-z -2[0,0,1]1/4,-3/4,00,0,0
-y-1/4,x-1/2,-z-1/4 -4^-1[0,0,1]0,0,01/8,-3/8,-1/8
-x,y-1/4,z+1/4 -2[1,0,0]0,-1/4,1/40,0,0
-y+1/4,-x-3/4,z -2[1,1,0]1/2,-1/2,0-1/4,0,0
x-1/4,-y-1/2,z-1/4 -2[0,1,0]-1/4,0,-1/40,-1/4,0
y+1/2,x,z+1/2 -2[-1,1,0]1/4,1/4,1/21/4,0,0
x+1/2,y+1/2,z 1---
-y+1,x+3/4,z+1/4 4^1[0,0,1]0,0,1/41/8,7/8,0
-x+3/4,-y+5/4,z+1/2 2[0,0,1]0,0,1/23/8,5/8,0
y+5/4,-x+1,z+3/4 4^-1[0,0,1]0,0,3/49/8,-1/8,0
x+1,-y+3/4,-z+1/4 2[1,0,0]1,0,00,3/8,1/8
y+3/4,x+5/4,-z+1/2 2[1,1,0]1,1,0-1/4,0,1/4
-x+5/4,y+1,-z+3/4 2[0,1,0]0,1,05/8,0,3/8
-y+1/2,-x+1/2,-z 2[-1,1,0]0,0,01/2,0,0
-x+1/2,-y+1/2,-z -1--1/4,1/4,0
y,-x+1/4,-z-1/4 -4^1[0,0,1]0,0,01/8,1/8,-1/8
x+1/4,y-1/4,-z-1/2 -2[0,0,1]1/4,-1/4,00,0,-1/4
-y-1/4,x,-z-3/4 -4^-1[0,0,1]0,0,0-1/8,-1/8,-3/8
-x,y+1/4,z-1/4 -2[1,0,0]0,1/4,-1/40,0,0
-y+1/4,-x-1/4,z-1/2 -2[1,1,0]1/4,-1/4,-1/20,0,0
x-1/4,-y,z-3/4 -2[0,1,0]-1/4,0,-3/40,0,0
y+1/2,x+1/2,z -2[-1,1,0]1/2,1/2,00,0,0 

Space group number: 141
Conventional Hermann-Mauguin symbol: I 41/a m d :2
Universal    Hermann-Mauguin symbol: I 41/a m d :2 (a+b,-a+b,c)
Hall symbol: -I 4bd 2 (1/2*x+1/2*y,-1/2*x+1/2*y,z)
Change-of-basis matrix: x-y,x+y,z
               Inverse: 1/2*x+1/2*y,-1/2*x+1/2*y,z

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
i641x,y,z
h32mx,x,z
g322x,1/8,-1/8
f322x,-x,0
e16mm21/8,1/8,z
d162/m0,0,1/2
c162/m0,0,0
b8-42m1/8,1/8,3/8
a8-42m-1/8,-1/8,1/8 

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

Grid factors implied by symmetries:
  Space group: (4, 4, 4)
  Structure-seminvariant vectors and moduli: (2, 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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