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Result of symbol lookup:
  Space group number: 135
  Schoenflies symbol: D4h^13
  Hermann-Mauguin symbol: P 42/m b c
  Hall symbol: -P 4c 2ab

Input space group symbol: P 42/m b c
Convention: Default

Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 16

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

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y,x,z+1/2 4^1[0,0,1]0,0,1/20,0,0
-x,-y,z 2[0,0,1]0,0,00,0,0
y,-x,z+1/2 4^-1[0,0,1]0,0,1/20,0,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
y+1/2,x+1/2,-z+1/2 2[1,1,0]1/2,1/2,00,0,1/4
-x+1/2,y+1/2,-z 2[0,1,0]0,1/2,01/4,0,0
-y+1/2,-x+1/2,-z+1/2 2[-1,1,0]0,0,01/2,0,1/4
-x,-y,-z -1--0,0,0
y,-x,-z-1/2 -4^1[0,0,1]0,0,00,0,-1/4
x,y,-z -2[0,0,1]0,0,00,0,0
-y,x,-z-1/2 -4^-1[0,0,1]0,0,00,0,-1/4
-x-1/2,y-1/2,z -2[1,0,0]0,-1/2,0-1/4,0,0
-y-1/2,-x-1/2,z-1/2 -2[1,1,0]0,0,-1/2-1/2,0,0
x-1/2,-y-1/2,z -2[0,1,0]-1/2,0,00,-1/4,0
y-1/2,x-1/2,z-1/2 -2[-1,1,0]-1/2,-1/2,-1/20,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
i161x,y,z
h8mx,y,0
g82x,x+1/2,1/4
f820,1/2,z
e820,0,z
d42220,1/2,1/4
c42/m0,1/2,0
b4-40,0,1/4
a42/m0,0,0

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

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: (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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