# coneToPolyhedron -- converts a cone to class Polyhedron

## Synopsis

• Usage:
P = coneToPolyhedron C
• Inputs:
• Outputs:

## 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

## Ways to use coneToPolyhedron :

• "coneToPolyhedron(Cone)"

## For the programmer

The object coneToPolyhedron is .