# normalFan -- computes the normalFan of a polyhedron

## Synopsis

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

## Description

The normalFan of a Polyhedron is the fan generated by the cones C_v for all vertices v of the Polyhedron, where C_v is the dual Cone of the positive Hull of P-v. If P is compact, i.e. a polytope, then the normalFan is complete.

 i1 : P = convexHull matrix{{1,0,0},{0,1,0}} o1 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 3 number of rays => 0 number of vertices => 3 o1 : Polyhedron i2 : F = normalFan P o2 = {ambient dimension => 2 } number of generating cones => 3 number of rays => 3 top dimension of the cones => 2 o2 : Fan i3 : apply(maxCones F,rays) o3 = {| 1 0 |, | -1 0 |, | 1 -1 |} | 0 1 | | -1 1 | | 0 -1 | o3 : List

## Ways to use normalFan :

• "normalFan(Polyhedron)"

## For the programmer

The object normalFan is .