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Input space group symbol: -F 4 2a
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,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]1/4,1/4,0-1/4,0,0
-x+1/2,y,-z 2[0,1,0]0,0,01/4,0,0
-y,-x+1/2,-z 2[-1,1,0]-1/4,1/4,01/4,0,0
-x,-y,-z -1--0,0,0
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]0,0,0-1/4,0,0
-y,-x-1/2,z -2[1,1,0]1/4,-1/4,0-1/4,0,0
x-1/2,-y,z -2[0,1,0]-1/2,0,00,0,0
y,x-1/2,z -2[-1,1,0]-1/4,-1/4,01/4,0,0
x,y+1/2,z+1/2 1---
-y,x+1/2,z+1/2 4^1[0,0,1]0,0,1/2-1/4,1/4,0
-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]0,0,1/21/4,1/4,0
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]1/2,1/2,0-1/2,0,1/4
-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]-1/2,1/2,01/2,0,1/4
-x,-y+1/2,-z+1/2 -1--0,1/4,1/4
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]0,1/2,00,0,1/4
-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]0,1/2,1/2-1/4,0,0
-y,-x,z+1/2 -2[1,1,0]0,0,1/20,0,0
x-1/2,-y+1/2,z+1/2 -2[0,1,0]-1/2,0,1/20,1/4,0
y,x,z+1/2 -2[-1,1,0]0,0,1/20,0,0
x+1/2,y,z+1/2 1---
-y+1/2,x,z+1/2 4^1[0,0,1]0,0,1/21/4,1/4,0
-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]0,0,1/21/4,-1/4,0
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]1/2,1/2,00,0,1/4
-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]0,0,01/2,0,1/4
-x+1/2,-y,-z+1/2 -1--1/4,0,1/4
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]1/2,0,00,0,1/4
-y+1/2,x,-z+1/2 -4^-1[0,0,1]0,0,01/4,1/4,1/4
-x,y,z+1/2 -2[1,0,0]0,0,1/20,0,0
-y+1/2,-x-1/2,z+1/2 -2[1,1,0]1/2,-1/2,1/20,0,0
x,-y,z+1/2 -2[0,1,0]0,0,1/20,0,0
y+1/2,x-1/2,z+1/2 -2[-1,1,0]0,0,1/21/2,0,0
x+1/2,y+1/2,z 1---
-y+1/2,x+1/2,z 4^1[0,0,1]0,0,00,1/2,0
-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]0,0,01/2,0,0
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]3/4,3/4,0-1/4,0,0
-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]-1/4,1/4,03/4,0,0
-x+1/2,-y+1/2,-z -1--1/4,1/4,0
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]1/2,1/2,00,0,0
-y+1/2,x+1/2,-z -4^-1[0,0,1]0,0,00,1/2,0
-x,y+1/2,z -2[1,0,0]0,1/2,00,0,0
-y+1/2,-x,z -2[1,1,0]1/4,-1/4,01/4,0,0
x,-y+1/2,z -2[0,1,0]0,0,00,1/4,0
y+1/2,x,z -2[-1,1,0]1/4,1/4,01/4,0,0

Space group number: 140
Conventional Hermann-Mauguin symbol: I 4/m c m
Universal    Hermann-Mauguin symbol: I 4/m c m (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
m641x,y,z
l32mx,1/4,z
k32mx,y,0
j322x,-x,1/4
i322x,0,1/4
h16mm2x,1/4,0
g16mm21/4,1/4,z
f1640,0,z
e162/m1/4,0,1/4
d8mmm1/4,1/4,0
c84/m0,0,0
b8-42m1/4,1/4,1/4
a84220,0,1/4

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

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: (2, 2, 2)
  Structure-seminvariant vectors and moduli: (2, 1, 1)
  Euclidean normalizer: (2, 2, 2)

  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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