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PolyhedralObject -- the class of all polyhedral objects in Polyhedra

Description

PolyhedralObject is the parent class of the three polyhedral objects in Polyhedra: 
i1 : convexHull matrix {{1,1,0,0},{1,0,1,0}}

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o1 : Polyhedron
 
i2 : posHull matrix {{1,2},{2,1}}

o2 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of the cone => 2
      number of facets => 2
      number of rays => 2

o2 : Cone
 
i3 : hirzebruch 3

o3 = {ambient dimension => 2         }
      number of generating cones => 4
      number of rays => 4
      top dimension of the cones => 2

o3 : Fan

Types of PolyhedralObject:

  • Cone -- the class of all rational convex polyhedral cones
  • Fan -- the class of all fans
  • PolyhedralComplex -- the class of all polyhedral complexes
  • Polyhedron -- the class of all convex polyhedra

Functions and methods returning an object of class PolyhedralObject:

  • faceOf (missing documentation)

Methods that use an object of class PolyhedralObject:

  • ambDim(PolyhedralObject) -- see ambDim -- ambient dimension of a Polyhedron, Cone or Fan
  • isSimplicial(PolyhedralObject) -- see isSimplicial -- checks if a polyhedral object is simplicial

For the programmer

The object PolyhedralObject is a type, with ancestor classes HashTable < Thing.

The source of this document is in OldPolyhedra.m2:4514:0.