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# polytope -- returns a polytope of which the fan is the normal fan if it is polytopal

## Synopsis

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

## Description

If the fan F is polytopal then polytope returns a polytope P. F is the normal fan of this polytope. Note that such a polytope is not unique.
 i1 : F = fan {posHull matrix {{1,0},{0,1}},posHull matrix {{0,-1},{1,1}},posHull matrix {{-1,-1},{0,1}},posHull matrix {{-1,1},{0,-1}},posHull matrix {{1,1},{0,-1}}} o1 = {ambient dimension => 2 } number of generating cones => 5 number of rays => 5 top dimension of the cones => 2 o1 : Fan i2 : P = polytope F {({ambient dimension => 2 }, {1, 2, 3, 4, 5})} dimension of lineality space => 0 dimension of the cone => 0 number of facets => 0 number of rays => 0 v: {{ambient dimension => 2 }, {ambient dimension => 2 }, {ambient dimension => 2 }, {ambient dimension => 2 }} dimension of lineality space => 0 dimension of lineality space => 0 dimension of lineality space => 0 dimension of lineality space => 0 dimension of the cone => 2 dimension of the cone => 2 dimension of the cone => 2 dimension of the cone => 2 number of facets => 2 number of facets => 2 number of facets => 2 number of facets => 2 number of rays => 2 number of rays => 2 number of rays => 2 number of rays => 2 o2 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 5 number of rays => 0 number of vertices => 5 o2 : Polyhedron

## Ways to use polytope :

• "polytope(Fan)"

## For the programmer

The object polytope is .