Every polyhedron P can be uniquely decomposed into the sum of a polytope and a cone, the tail or recession cone of P. Thus, it is the cone generated by the non-compact part, i.e. the rays and the lineality space of P. If P is a polytope then the tail cone is the origin in the ambient space of P.
i1 : P = intersection(matrix{{-1,0},{1,0},{0,-1},{-1,-1},{1,-1}},matrix{{2},{2},{-1},{0},{0}})
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 5
number of rays => 1
number of vertices => 4
o1 : Polyhedron
i2 : C = tailCone P
o2 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of the cone => 1
number of facets => 1
number of rays => 1
o2 : Cone