# 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 the relative interior.

 i1 : P = hypercube 2 o1 = P o1 : Polyhedron i2 : F = faceFan P o2 = F o2 : Fan i3 : raysF = rays F o3 = | -1 1 -1 1 | | -1 -1 1 1 | 2 4 o3 : Matrix ZZ <--- ZZ i4 : apply(maxCones F, mc -> raysF_mc) o4 = {| -1 -1 |, | 1 1 |, | -1 1 |, | -1 1 |} | -1 1 | | -1 1 | | -1 -1 | | 1 1 | o4 : List

## Ways to use faceFan :

• "faceFan(Polyhedron)"

## For the programmer

The object faceFan is .