vertexFacetMatrix -- computes the vertex-facet-relations matrix

Synopsis

• Usage:

  M = vertexFacetMatrix P

• Inputs:
  • P, a convex polyhedron
• Outputs:
  • M, a matrix

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 = P

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