# normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of a polyhedron

## Description

The normal cone of a face Q of a polyhedron P is the cone in the normal fan (see normalFan) that corresponds to this face. This is the cone of all vectors attaining their maximum on this face.

 i1 : P = hypercube 3 o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 8 o1 : Polyhedron i2 : Q = convexHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}} o2 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o2 : Polyhedron i3 : C = normalCone(P,Q) o3 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of the cone => 1 number of facets => 1 number of rays => 1 o3 : Cone i4 : rays C o4 = | 0 | | 0 | | -1 | 3 1 o4 : Matrix ZZ <--- ZZ