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Result of symbol lookup:
  Space group number: 4
  Schoenflies symbol: C2^2
  Hermann-Mauguin symbol: P 1 21 1
  Unique axis: b
  Hall symbol: P 2yb

Input space group symbol: P 1 21 1
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Number of representative symmetry operations: 2
Total number of symmetry operations: 2

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

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

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
a21x,y,z

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 3
    Vector    Modulus
    (1, 0, 0) 2
    (0, 1, 0) 0
    (0, 0, 1) 2
  Inversion through a centre at: 0,0,0

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