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Input space group symbol: -F 4auw
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+3/4,x,z+1/4 4^1[0,0,1]0,0,1/43/8,3/8,0
-x+3/4,-y+3/4,z+1/2 2[0,0,1]0,0,1/23/8,3/8,0
y,-x+3/4,z+3/4 4^-1[0,0,1]0,0,3/43/8,3/8,0
-x,-y,-z -1--0,0,0
y-3/4,-x,-z-1/4 -4^1[0,0,1]0,0,0-3/8,3/8,-1/8
x-3/4,y-3/4,-z-1/2 -2[0,0,1]-3/4,-3/4,00,0,-1/4
-y,x-3/4,-z-3/4 -4^-1[0,0,1]0,0,03/8,-3/8,-3/8
x,y+1/2,z+1/2 1---
-y+3/4,x+1/2,z+3/4 4^1[0,0,1]0,0,3/41/8,5/8,0
-x+3/4,-y+5/4,z+1 2[0,0,1]0,0,13/8,5/8,0
y,-x+5/4,z+5/4 4^-1[0,0,1]0,0,5/45/8,5/8,0
-x,-y+1/2,-z+1/2 -1--0,1/4,1/4
y-3/4,-x+1/2,-z+1/4 -4^1[0,0,1]0,0,0-1/8,5/8,1/8
x-3/4,y-1/4,-z -2[0,0,1]-3/4,-1/4,00,0,0
-y,x-1/4,-z-1/4 -4^-1[0,0,1]0,0,01/8,-1/8,-1/8
x+1/2,y,z+1/2 1---
-y+5/4,x,z+3/4 4^1[0,0,1]0,0,3/45/8,5/8,0
-x+5/4,-y+3/4,z+1 2[0,0,1]0,0,15/8,3/8,0
y+1/2,-x+3/4,z+5/4 4^-1[0,0,1]0,0,5/45/8,1/8,0
-x+1/2,-y,-z+1/2 -1--1/4,0,1/4
y-1/4,-x,-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+1/2,x-3/4,-z-1/4 -4^-1[0,0,1]0,0,05/8,-1/8,-1/8
x+1/2,y+1/2,z 1---
-y+5/4,x+1/2,z+1/4 4^1[0,0,1]0,0,1/43/8,7/8,0
-x+5/4,-y+5/4,z+1/2 2[0,0,1]0,0,1/25/8,5/8,0
y+1/2,-x+5/4,z+3/4 4^-1[0,0,1]0,0,3/47/8,3/8,0
-x+1/2,-y+1/2,-z -1--1/4,1/4,0
y-1/4,-x+1/2,-z-1/4 -4^1[0,0,1]0,0,01/8,3/8,-1/8
x-1/4,y-1/4,-z-1/2 -2[0,0,1]-1/4,-1/4,00,0,-1/4
-y+1/2,x-1/4,-z-3/4 -4^-1[0,0,1]0,0,03/8,1/8,-3/8

Space group number: 88
Conventional Hermann-Mauguin symbol: I 41/a :2
Universal    Hermann-Mauguin symbol: I 41/a :2 (a-b,a+b,c)
Hall symbol: -I 4ad (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
f321x,y,z
e162-1/8,1/8,z
d16-10,0,1/2
c16-10,0,0
b8-4-1/8,1/8,-3/8
a8-4-1/8,1/8,1/8

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

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,y+1/4,z+1/4 -2[1,0,0]0,1/4,1/40,0,0

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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