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Result of symbol lookup:
  Space group number: 61
  Schoenflies symbol: D2h^15
  Hermann-Mauguin symbol: P b c a
  Hall symbol: -P 2ac 2ab

Input space group symbol: P b c a
Convention: Default

Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 8

Parallelepiped containing an asymmetric unit:
  0<=x<1/2; 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---
-x+1/2,-y,z+1/2 2[0,0,1]0,0,1/21/4,0,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
-x,y+1/2,-z+1/2 2[0,1,0]0,1/2,00,0,1/4
-x,-y,-z -1--0,0,0
x-1/2,y,-z-1/2 -2[0,0,1]-1/2,0,00,0,-1/4
-x-1/2,y-1/2,z -2[1,0,0]0,-1/2,0-1/4,0,0
x,-y-1/2,z-1/2 -2[0,1,0]0,0,-1/20,-1/4,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
c81x,y,z
b4-10,0,1/2
a4-10,0,0

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

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

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