# maxCones -- displays the generating Cones of a Fan

## Synopsis

• Usage:
L = maxCones F
• Inputs:
• F, an instance of the type Fan
• Outputs:

## Description

maxCones displays the List of generating cones of the Fan, i.e. all Cones that are not a face of one of the other cones. These are all of the same dimension if and only if the Fan is pure (see: isPure).

 i1 : F = normalFan crossPolytope 3 o1 = {ambient dimension => 3 } number of generating cones => 6 number of rays => 8 top dimension of the cones => 3 o1 : Fan i2 : L = maxCones F o2 = {{ambient dimension => 3 }, {ambient dimension => 3 dimension of lineality space => 0 dimension of lineality space => dimension of the cone => 3 dimension of the cone => 3 number of facets => 4 number of facets => 4 number of rays => 4 number of rays => 4 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, {ambient dimension => 3 0 dimension of lineality space => 0 dimension of lineality space dimension of the cone => 3 dimension of the cone => 3 number of facets => 4 number of facets => 4 number of rays => 4 number of rays => 4 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, => 0 dimension of lineality space => 0 dimension of the cone => 3 number of facets => 4 number of rays => 4 ------------------------------------------------------------------------ {ambient dimension => 3 }} dimension of lineality space => 0 dimension of the cone => 3 number of facets => 4 number of rays => 4 o2 : List i3 : apply(L,rays) o3 = {| -1 1 -1 1 |, | -1 1 -1 1 |, | -1 -1 -1 -1 |, | -1 1 -1 1 |, | -1 | -1 -1 1 1 | | -1 -1 -1 -1 | | -1 1 -1 1 | | -1 -1 1 1 | | 1 | -1 -1 -1 -1 | | -1 -1 1 1 | | -1 -1 1 1 | | 1 1 1 1 | | -1 ------------------------------------------------------------------------ 1 -1 1 |, | 1 1 1 1 |} 1 1 1 | | -1 1 -1 1 | -1 1 1 | | -1 -1 1 1 | o3 : List

## Ways to use maxCones :

• "maxCones(Fan)"

## For the programmer

The object maxCones is .