[Index of services] [New input] 
Input space group symbol: F 4d -2d
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+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 -2[1,0,0]0,1/4,1/41/8,0,0
-y,-x+1/2,z+1/2 -2[1,1,0]-1/4,1/4,1/21/4,0,0
x+3/4,-y+1/4,z+3/4 -2[0,1,0]3/4,0,3/40,1/8,0
y,x,z -2[-1,1,0]0,0,00,0,0
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 -2[1,0,0]0,3/4,3/41/8,0,0
-y,-x+1,z+1 -2[1,1,0]-1/2,1/2,11/2,0,0
x+3/4,-y+3/4,z+5/4 -2[0,1,0]3/4,0,5/40,3/8,0
y,x+1/2,z+1/2 -2[-1,1,0]1/4,1/4,1/2-1/4,0,0
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 -2[1,0,0]0,1/4,3/43/8,0,0
-y+1/2,-x+1/2,z+1 -2[1,1,0]0,0,11/2,0,0
x+5/4,-y+1/4,z+5/4 -2[0,1,0]5/4,0,5/40,1/8,0
y+1/2,x,z+1/2 -2[-1,1,0]1/4,1/4,1/21/4,0,0
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 -2[1,0,0]0,3/4,1/43/8,0,0
-y+1/2,-x+1,z+1/2 -2[1,1,0]-1/4,1/4,1/23/4,0,0
x+5/4,-y+3/4,z+3/4 -2[0,1,0]5/4,0,3/40,3/8,0
y+1/2,x+1/2,z -2[-1,1,0]1/2,1/2,00,0,0 

Space group number: 109
Conventional Hermann-Mauguin symbol: I 41 m d
Universal    Hermann-Mauguin symbol: I 41 m d (a+b,-a+b,c)
Hall symbol:  I 4bw -2 (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
c321x,y,z
b16mx,x,z
a8mm20,0,z 

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
    (0, 0, 1) 0
  Inversion through a centre at: 1/8,-1/8,0

Grid factors implied by symmetries:
  Space group: (4, 4, 4)
  Structure-seminvariant vectors and moduli: (1, 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.
[Index of services] [New input]