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Input space group symbol: F 4d -1d
Convention: Hall symbol

Number of lattice translations: 4
Space group is centric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 32

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+1/4,x+1/4,z+1/4 4^1[0,0,1]0,0,1/40,1/4,0
-x,-y+1/2,z+1/2 2[0,0,1]0,0,1/20,1/4,0
y+3/4,-x+1/4,z+3/4 4^-1[0,0,1]0,0,3/41/2,-1/4,0
-x+1/4,-y+1/4,-z+1/4 -1--1/8,1/8,1/8
y,-x,-z -4^1[0,0,1]0,0,00,0,0
x+1/4,y-1/4,-z-1/4 -2[0,0,1]1/4,-1/4,00,0,-1/8
-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 1---
-y+1/4,x+3/4,z+3/4 4^1[0,0,1]0,0,3/4-1/4,1/2,0
-x,-y+1,z+1 2[0,0,1]0,0,10,1/2,0
y+3/4,-x+3/4,z+5/4 4^-1[0,0,1]0,0,5/43/4,0,0
-x+1/4,-y+3/4,-z+3/4 -1--1/8,3/8,3/8
y,-x+1/2,-z+1/2 -4^1[0,0,1]0,0,01/4,1/4,1/4
x+1/4,y+1/4,-z+1/4 -2[0,0,1]1/4,1/4,00,0,1/8
-y-1/2,x+1/2,-z -4^-1[0,0,1]0,0,0-1/2,0,0
x+1/2,y,z+1/2 1---
-y+3/4,x+1/4,z+3/4 4^1[0,0,1]0,0,3/41/4,1/2,0
-x+1/2,-y+1/2,z+1 2[0,0,1]0,0,11/4,1/4,0
y+5/4,-x+1/4,z+5/4 4^-1[0,0,1]0,0,5/43/4,-1/2,0
-x+3/4,-y+1/4,-z+3/4 -1--3/8,1/8,3/8
y+1/2,-x,-z+1/2 -4^1[0,0,1]0,0,01/4,-1/4,1/4
x+3/4,y-1/4,-z+1/4 -2[0,0,1]3/4,-1/4,00,0,1/8
-y,x,-z -4^-1[0,0,1]0,0,00,0,0
x+1/2,y+1/2,z 1---
-y+3/4,x+3/4,z+1/4 4^1[0,0,1]0,0,1/40,3/4,0
-x+1/2,-y+1,z+1/2 2[0,0,1]0,0,1/21/4,1/2,0
y+5/4,-x+3/4,z+3/4 4^-1[0,0,1]0,0,3/41,-1/4,0
-x+3/4,-y+3/4,-z+1/4 -1--3/8,3/8,1/8
y+1/2,-x+1/2,-z -4^1[0,0,1]0,0,01/2,0,0
x+3/4,y+1/4,-z-1/4 -2[0,0,1]3/4,1/4,00,0,-1/8
-y,x+1/2,-z-1/2 -4^-1[0,0,1]0,0,0-1/4,1/4,-1/4 

Space group number: 88
Conventional Hermann-Mauguin symbol: I 41/a :2
Universal    Hermann-Mauguin symbol: I 41/a :2 (a+b,-a+b-1/4,c-1/8)
Hall symbol: -I 4ad (1/2*x+1/2*y+1/8,-1/2*x+1/2*y+1/8,z+1/8)
Change-of-basis matrix: x-y,x+y-1/4,z-1/8
               Inverse: 1/2*x+1/2*y+1/8,-1/2*x+1/2*y+1/8,z+1/8

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
f321x,y,z
e1621/4,1/4,z
d16-11/8,1/8,5/8
c16-11/8,1/8,1/8
b8-41/4,1/4,-1/4
a8-41/4,1/4,1/4 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 0, 0) 2
  Further generators:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x+1/4,-y+1/4,z+1/4 -2[0,1,0]1/4,0,1/40,1/8,0 

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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