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: