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OldPolyhedra :: polytope

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

Synopsis

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 :

For the programmer

The object polytope is a method function.