# vertexFacetMatrix -- computes the vertex-facet-relations matrix

## Synopsis

• Usage:
M = vertexFacetMatrix P
• Inputs:
• Outputs:
• M,

## Description

vertexFacetMatrix computes the matrix M where the columns are indexed by the facets and the rows are indexed by the vertices of P and has 1 as an entry if the corresponding facet contains this vertex and 0 otherwise.

 i1 : P = cyclicPolytope(3,5) o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 5 o1 : Polyhedron i2 : vertexFacetMatrix P o2 = | 0 1 2 3 4 5 6 | | 1 1 1 1 0 0 1 | | 2 1 0 0 0 1 1 | | 3 1 1 0 1 1 0 | | 4 0 1 1 1 0 0 | | 5 0 0 1 1 1 1 | 6 7 o2 : Matrix ZZ <--- ZZ

## Ways to use vertexFacetMatrix :

• "vertexFacetMatrix(Polyhedron)"

## For the programmer

The object vertexFacetMatrix is .