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Input space group symbol: F 4ad 2
Convention: Hall symbol

Number of lattice translations: 4
Space group is acentric.
Space group is chiral.
Number of representative symmetry operations: 8
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+1/4,z+1/4 4^1[0,0,1]0,0,1/41/4,1/2,0
-x+1/2,-y,z+1/2 2[0,0,1]0,0,1/21/4,0,0
y+3/4,-x+3/4,z+3/4 4^-1[0,0,1]0,0,3/43/4,0,0
x,-y,-z 2[1,0,0]0,0,00,0,0
y+3/4,x+1/4,-z+1/4 2[1,1,0]1/2,1/2,01/4,0,1/8
-x+1/2,y,-z+1/2 2[0,1,0]0,0,01/4,0,1/4
-y+3/4,-x+3/4,-z+3/4 2[-1,1,0]0,0,03/4,0,3/8
x,y+1/2,z+1/2 1---
-y+3/4,x+3/4,z+3/4 4^1[0,0,1]0,0,3/40,3/4,0
-x+1/2,-y+1/2,z+1 2[0,0,1]0,0,11/4,1/4,0
y+3/4,-x+5/4,z+5/4 4^-1[0,0,1]0,0,5/41,1/4,0
x,-y+1/2,-z+1/2 2[1,0,0]0,0,00,1/4,1/4
y+3/4,x+3/4,-z+3/4 2[1,1,0]3/4,3/4,00,0,3/8
-x+1/2,y+1/2,-z+1 2[0,1,0]0,1/2,01/4,0,1/2
-y+3/4,-x+5/4,-z+5/4 2[-1,1,0]-1/4,1/4,01,0,5/8
x+1/2,y,z+1/2 1---
-y+5/4,x+1/4,z+3/4 4^1[0,0,1]0,0,3/41/2,3/4,0
-x+1,-y,z+1 2[0,0,1]0,0,11/2,0,0
y+5/4,-x+3/4,z+5/4 4^-1[0,0,1]0,0,5/41,-1/4,0
x+1/2,-y,-z+1/2 2[1,0,0]1/2,0,00,0,1/4
y+5/4,x+1/4,-z+3/4 2[1,1,0]3/4,3/4,01/2,0,3/8
-x+1,y,-z+1 2[0,1,0]0,0,01/2,0,1/2
-y+5/4,-x+3/4,-z+5/4 2[-1,1,0]1/4,-1/4,01,0,5/8
x+1/2,y+1/2,z 1---
-y+5/4,x+3/4,z+1/4 4^1[0,0,1]0,0,1/41/4,1,0
-x+1,-y+1/2,z+1/2 2[0,0,1]0,0,1/21/2,1/4,0
y+5/4,-x+5/4,z+3/4 4^-1[0,0,1]0,0,3/45/4,0,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
y+5/4,x+3/4,-z+1/4 2[1,1,0]1,1,01/4,0,1/8
-x+1,y+1/2,-z+1/2 2[0,1,0]0,1/2,01/2,0,1/4
-y+5/4,-x+5/4,-z+3/4 2[-1,1,0]0,0,05/4,0,3/8 

Space group number: 98
Conventional Hermann-Mauguin symbol: I 41 2 2
Universal    Hermann-Mauguin symbol: I 41 2 2 (a-b,a+b,c)
Hall symbol:  I 4bw 2bw (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
g321x,y,z
f162x,x+1/4,1/8
e162x,0,0
d1620,y,0
c1620,0,z
b82220,0,1/2
a82220,0,0 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 0, 0) 2
  Inversion through a centre at: 1/8,1/8,1/8

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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