# maxFace -- computes the face of a Polyhedron or Cone where a weight attains its maximum

## Synopsis

• Usage:
F = maxFace(w,P)
F = maxFace(w,C)
• Inputs:
• w, , over ZZ or QQ with only one column representing a weight vector
• Outputs:
• F, Depending on the input, a Cone or a Polyhedron, the face where w attains its maximum

## Description

maxFace computes the face of the given Polyhedron P or Cone C where w attains its maximum.

 i1 : P = crossPolytope 3 o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 8 number of rays => 0 number of vertices => 6 o1 : Polyhedron i2 : w = matrix {{1},{-1},{0}} o2 = | 1 | | -1 | | 0 | 3 1 o2 : Matrix ZZ <--- ZZ i3 : F = maxFace(w,P) o3 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 1 number of facets => 2 number of rays => 0 number of vertices => 2 o3 : Polyhedron i4 : vertices F o4 = | 1 0 | | 0 -1 | | 0 0 | 3 2 o4 : Matrix QQ <--- QQ

## Ways to use maxFace :

• "maxFace(Matrix,Cone)"
• "maxFace(Matrix,Polyhedron)"

## For the programmer

The object maxFace is .