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

Number of lattice translations: 4
Space group is acentric.
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,-x,-z -4^1[0,0,1]0,0,00,0,0
-x,-y,z 2[0,0,1]0,0,00,0,0
-y,x,-z -4^-1[0,0,1]0,0,00,0,0
x+1/2,-y,-z 2[1,0,0]1/2,0,00,0,0
-y,-x+1/2,z -2[1,1,0]-1/4,1/4,01/4,0,0
-x+1/2,y,-z 2[0,1,0]0,0,01/4,0,0
y,x+1/2,z -2[-1,1,0]1/4,1/4,0-1/4,0,0
x,y+1/2,z+1/2 1---
y,-x+1/2,-z+1/2 -4^1[0,0,1]0,0,01/4,1/4,1/4
-x,-y+1/2,z+1/2 2[0,0,1]0,0,1/20,1/4,0
-y,x+1/2,-z+1/2 -4^-1[0,0,1]0,0,0-1/4,1/4,1/4
x+1/2,-y+1/2,-z+1/2 2[1,0,0]1/2,0,00,1/4,1/4
-y,-x+1,z+1/2 -2[1,1,0]-1/2,1/2,1/21/2,0,0
-x+1/2,y+1/2,-z+1/2 2[0,1,0]0,1/2,01/4,0,1/4
y,x+1,z+1/2 -2[-1,1,0]1/2,1/2,1/2-1/2,0,0
x+1/2,y,z+1/2 1---
y+1/2,-x,-z+1/2 -4^1[0,0,1]0,0,01/4,-1/4,1/4
-x+1/2,-y,z+1/2 2[0,0,1]0,0,1/21/4,0,0
-y+1/2,x,-z+1/2 -4^-1[0,0,1]0,0,01/4,1/4,1/4
x+1,-y,-z+1/2 2[1,0,0]1,0,00,0,1/4
-y+1/2,-x+1/2,z+1/2 -2[1,1,0]0,0,1/21/2,0,0
-x+1,y,-z+1/2 2[0,1,0]0,0,01/2,0,1/4
y+1/2,x+1/2,z+1/2 -2[-1,1,0]1/2,1/2,1/20,0,0
x+1/2,y+1/2,z 1---
y+1/2,-x+1/2,-z -4^1[0,0,1]0,0,01/2,0,0
-x+1/2,-y+1/2,z 2[0,0,1]0,0,01/4,1/4,0
-y+1/2,x+1/2,-z -4^-1[0,0,1]0,0,00,1/2,0
x+1,-y+1/2,-z 2[1,0,0]1,0,00,1/4,0
-y+1/2,-x+1,z -2[1,1,0]-1/4,1/4,03/4,0,0
-x+1,y+1/2,-z 2[0,1,0]0,1/2,01/2,0,0
y+1/2,x+1,z -2[-1,1,0]3/4,3/4,0-1/4,0,0

Space group number: 120
Conventional Hermann-Mauguin symbol: I -4 c 2
Universal    Hermann-Mauguin symbol: I -4 c 2 (a+b,-a+b,c)
Hall symbol:  I -4 -2c (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
i321x,y,z
h162x,1/4,0
g1621/4,1/4,z
f1620,0,z
e162x,0,1/4
d82221/4,1/4,0
c8-41/4,1/4,1/4
b8-40,0,0
a82220,0,1/4

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 1, 1) 4
  Inversion through a centre at: 0,0,0

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