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Result of symbol lookup:
  Space group number: 122
  Schoenflies symbol: D2d^12
  Hermann-Mauguin symbol: I -4 2 d
  Hall symbol: I -4 2bw

Input space group symbol: I -4 2 d
Convention: Default

Number of lattice translations: 2
Space group is acentric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 16

Parallelepiped containing an asymmetric unit:
  0<=x<=1/4; 0<=y<=1/4; 0<=z<1

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,-y+1/2,-z+1/4 2[1,0,0]0,0,00,1/4,1/8
-y+1/2,-x,z+3/4 -2[1,1,0]1/4,-1/4,3/41/4,0,0
-x,y+1/2,-z+1/4 2[0,1,0]0,1/2,00,0,1/8
y+1/2,x,z+3/4 -2[-1,1,0]1/4,1/4,3/41/4,0,0
x+1/2,y+1/2,z+1/2 1---
y+1/2,-x+1/2,-z+1/2 -4^1[0,0,1]0,0,01/2,0,1/4
-x+1/2,-y+1/2,z+1/2 2[0,0,1]0,0,1/21/4,1/4,0
-y+1/2,x+1/2,-z+1/2 -4^-1[0,0,1]0,0,00,1/2,1/4
x+1/2,-y+1,-z+3/4 2[1,0,0]1/2,0,00,1/2,3/8
-y+1,-x+1/2,z+5/4 -2[1,1,0]1/4,-1/4,5/43/4,0,0
-x+1/2,y+1,-z+3/4 2[0,1,0]0,1,01/4,0,3/8
y+1,x+1/2,z+5/4 -2[-1,1,0]3/4,3/4,5/41/4,0,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
e161x,y,z
d82x,1/4,1/8
c820,0,z
b4-40,0,1/2
a4-40,0,0 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2
  Inversion through a centre at: 1/4,0,1/8

Grid factors implied by symmetries:
  Space group: (2, 2, 4)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (2, 2, 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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