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Result of symbol lookup:
  Space group number: 91
  Schoenflies symbol: D4^3
  Hermann-Mauguin symbol: P 41 2 2
  Hall symbol: P 4w 2c

Input space group symbol: P 41 2 2
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 8
Total number of symmetry operations: 8

Parallelepiped containing an asymmetric unit:
  0<=x<=1/2; 0<=y<=1/2; -1/8<=z<=3/8

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y,x,z+1/4 4^1[0,0,1]0,0,1/40,0,0
-x,-y,z+1/2 2[0,0,1]0,0,1/20,0,0
y,-x,z+3/4 4^-1[0,0,1]0,0,3/40,0,0
x,-y,-z+1/2 2[1,0,0]0,0,00,0,1/4
y,x,-z+3/4 2[1,1,0]0,0,00,0,3/8
-x,y,-z 2[0,1,0]0,0,00,0,0
-y,-x,-z+1/4 2[-1,1,0]0,0,00,0,1/8

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
d81x,y,z
c42x,x,3/8
b421/2,y,0
a420,y,0

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 2
    Vector    Modulus
    (0, 0, 1) 2
    (1, 1, 0) 2

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