coneToPolyhedron -- converts a cone to class Polyhedron

Synopsis

• Usage:

  P = coneToPolyhedron C

• Inputs:
  • C, a convex rational cone
• Outputs:
  • P, a convex polyhedron

Description

Every Cone is in particular a Polyhedron. coneToPolyhedron converts the cone into the same cone but of class Polyhedron.

Consider the positive orthant in QQ^3:

i1 : C = posHull matrix {{1,0,0},{0,1,0},{0,0,1}}

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of the cone => 3
      number of facets => 3
      number of rays => 3

o1 : Cone

If we want to consider the positive orthant not as cone but as a polyhedron we apply coneToPolyhedron:

i2 : P = coneToPolyhedron C

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 3
      number of rays => 3
      number of vertices => 1

o2 : Polyhedron

Although, they are the same geometric object but of different classes, Polyhedra considers them not as equal:

i3 : P === C

o3 = false