# faceFan -- computes the fan generated by the cones over the faces

## Synopsis

• Usage:
F = faceFan P
• Inputs:
• Outputs:
• F, an instance of the type Fan

## Description

For a polyhedron with the origin in its relative interior, the face fan is the fan generated by the cones over the faces of the polytope. Hence the origin must be in hte relative interior.

 i1 : P = hypercube 2 o1 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o1 : Polyhedron i2 : F = faceFan P o2 = {ambient dimension => 2 } number of generating cones => 4 number of rays => 4 top dimension of the cones => 2 o2 : Fan i3 : apply(maxCones F, rays) o3 = {| -1 1 |, | -1 -1 |, | 1 1 |, | -1 1 |} | 1 1 | | -1 1 | | -1 1 | | -1 -1 | o3 : List

## Ways to use faceFan :

• "faceFan(Polyhedron)"

## For the programmer

The object faceFan is .