# tailCone -- computes the tail/recession cone of a polyhedron

## Synopsis

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

## Description

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 i3 : rays C o3 = | 0 | | 1 | 2 1 o3 : Matrix ZZ <--- ZZ

## Ways to use tailCone :

• "tailCone(Polyhedron)"

## For the programmer

The object tailCone is .