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# OldPolyhedra : Table of Contents

- OldPolyhedra -- for computations with convex polyhedra, cones, and fans
- addCone -- adds cones to a Fan
- addPolyhedron -- adds Polyhedra to a PolyhedralComplex
- affineHull -- computes the affine hull of a polyhedron
- affineImage -- computes the affine image of a cone or polyhedron
- affineImage(Matrix,Cone,Matrix) -- computes the affine image of a cone
- affineImage(Matrix,Polyhedron,Matrix) -- computes the affine image of a polyhedron
- affinePreimage -- computes the affine preimage of a cone or polyhedron
- affinePreimage(Matrix,Cone,Matrix) -- computes the affine preimage of a cone
- affinePreimage(Matrix,Polyhedron,Matrix) -- computes the affine preimage of a polyhedron
- ambDim -- ambient dimension of a Polyhedron, Cone or Fan
- areCompatible -- checks if the intersection of two cones/polyhedra is a face of each
- bipyramid -- computes the bipyramid over a polyhedron
- boundaryMap (missing documentation)
- ccRefinement -- computes the coarsest common refinement of a set of rays
- cellDecompose -- computes the regular cell decomposition
- commonFace -- checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans
- Cone -- the class of all rational convex polyhedral cones
- Cone * Cone -- computes the direct product of two cones
- Cone * Polyhedron -- computes the direct product of a cone and a polyhedron
- Cone + Cone -- computes the Minkowski sum of two cones
- Cone + Polyhedron -- computes the Minkowski sum of a cone and a polyhedron
- Cone == Cone -- equality
- Cone ? Cone -- compares the Cones
- cones -- computes all cones of a fan of a certain dimension
- coneToPolyhedron -- converts a cone to class Polyhedron
- contains -- checks if the first argument contains the second argument
- convexHull -- computing the convex hull of points, rays and polyhedra
- crossPolytope -- computes the d-dimensional crosspolytope with diameter 2s
- cyclicPolytope -- computes the d dimensional cyclic polytope with n vertices
- dim(Cone) -- computes the dimension of a cone
- dim(Fan) -- computes the dimension of a fan
- dim(PolyhedralComplex) -- computes the dimension of a polyhedral complex
- dim(Polyhedron) -- computes the dimension of a polyhedron
- directProduct -- computes the direct product of two convex objects
- directProduct(Cone,Cone) -- computes the direct product of polyhedra and cones
- directProduct(Fan,Fan) -- computes the direct product of two fans
- dualCayley (missing documentation)
- dualCayleyFace (missing documentation)
- dualCone -- computes the dual Cone
- dualFaceLattice -- computes the dual face lattice of a cone or polyhedron
- dualFaceLattice(ZZ,Cone) -- computes the dual face lattice of a cone
- dualFaceLattice(ZZ,Polyhedron) -- computes the dual face lattice of a polyhedron
- ehrhart -- calculates the Ehrhart polynomial of a polytope
- emptyPolyhedron -- generates the empty polyhedron in n-space
- faceFan -- computes the fan generated by the cones over the faces
- faceLattice -- computes the face lattice of a cone or polyhedron
- faceLattice(ZZ,Cone) -- computes the face lattice of a cone
- faceLattice(ZZ,Polyhedron) -- computes the face lattice of a polyhedron
- faceOf (missing documentation)
- faces -- computes all faces of a certain codimension of a Cone or Polyhedron
- Fan -- the class of all fans
- fan -- generates a Fan
- Fan * Fan -- computes the direct product
- Fan == Fan -- equality
- fVector -- computes the f-vector of a Cone or Polyhedron
- halfspaces -- computes the defining half-spaces of a Cone or a Polyhedron
- hilbertBasis -- computes the Hilbert basis of a Cone
- hirzebruch -- computes the fan of the r-th Hirzebruch surface
- hypercube -- computes the d-dimensional hypercube with edge length 2*s
- hyperplanes -- computes the defining hyperplanes of a Cone or a Polyhedron
- imageFan -- computes the fan of the image
- incompCones -- returns the pairs of incompatible cones
- incompPolyhedra -- returns the pairs of incompatible polyhedra
- inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron
- interiorLatticePoints -- computes the lattice points in the relative interior of a polytope
- interiorPoint -- computes a point in the relative interior of the Polyhedron
- interiorVector -- computes a vector in the relative interior of a Cone
- intersection -- computes the intersection of half-spaces, hyperplanes, cones, and polyhedra
- isCompact -- checks compactness of a Polyhedron
- isComplete -- checks completeness of a Fan or PolyhedralComplex
- isEmpty -- checks if a Polyhedron is empty
- isFace -- tests if the first argument is a face of the second
- isLatticePolytope -- checks if a polyhedron is a lattice polytope
- isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice
- isPointed -- checks if a Cone or Fan is pointed
- isPolytopal -- checks if a Fan is polytopal
- isPure -- checks if a Fan or PolyhedralComplex is of pure dimension
- isReflexive -- checks if a Polytope is reflexive
- isSimplicial -- checks if a polyhedral object is simplicial
- isSmooth(Cone) -- checks if a Cone or Fan is smooth
- isVeryAmple -- checks if the Polyhedron is very ample
- latticePoints -- computes the lattice points of a polytope
- linSpace -- computes a basis of the lineality space
- maxCones -- displays the generating Cones of a Fan
- maxFace -- computes the face of a Polyhedron or Cone where a weight attains its maximum
- maxPolyhedra -- displays the generating Polyhedra of a PolyhedralComplex
- minFace -- computes the face of a Polyhedron or Cone where a weight attains its minimum
- minkowskiSum -- computes the Minkowski sum of two convex objects
- minkSummandCone -- computes the Cone of all Minkowski summands and the minimal decompositions
- mixedVolume -- computes the mixed volume of a list of polytope
- net(Cone) -- displays characteristics of a cone
- net(Fan) -- displays characteristics of a fan
- net(PolyhedralComplex) -- displays characteristics of a polyhedral complex
- net(Polyhedron) -- displays characteristics of a polyhedron
- newtonPolytope -- computes the Newton polytope of a polynomial
- normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of a polyhedron
- normalFan -- computes the normalFan of a polyhedron
- objectiveVector -- computes an objective vector of a face of a polyhedron
- polar -- computes the polar of a polyhedron
- polarFace -- computes the dual face of the polar polyhedron
- polyhedra -- computes all polyhedra of a polyhedral complex of a certain dimension
- PolyhedralComplex -- the class of all polyhedral complexes
- polyhedralComplex -- generates a PolyhedralComplex
- PolyhedralObject -- the class of all polyhedral objects in Polyhedra
- Polyhedron -- the class of all convex polyhedra
- Polyhedron * Cone -- computes the direct product of a polyhedron and a cone
- Polyhedron * Polyhedron -- computes the direct product of two polyhedra
- Polyhedron + Cone -- computes the Minkowski sum of a polyhedron and a cone
- Polyhedron + Polyhedron -- computes the Minkowski sum of two polyhedra
- Polyhedron == Polyhedron -- equality
- polytope -- returns a polytope of which the fan is the normal fan if it is polytopal
- posHull -- computes the positive hull of rays, cones, and the cone over a polyhedron
- posOrthant -- generates the positive orthant in n-space
- proximum -- computes the proximum of the Polyhedron/Cone to a point in euclidian metric
- pyramid -- computes the pyramid over a polyhedron
- QQ * Polyhedron -- rescales a polyhedron by a given positive factor
- rays -- displays all rays of a Cone, a Fan, or a Polyhedron
- saveSession -- save the actual Polyhedra session to a file
- secondaryPolytope -- computes the secondary polytope of a compact polyhedron
- skeleton -- computes the k-skeleton of a Fan or PolyhedralComplex
- smallestFace -- determines the smallest face of the Cone/Polyhedron containing a point
- smoothSubfan -- computes the subfan of all smooth cones
- statePolytope -- computes the state polytope of a homogeneous ideal
- stdSimplex -- generates the d-dimensional standard simplex
- stellarSubdivision -- computes the stellar subdivision of the fan by a ray
- sublatticeBasis -- computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope
- tailCone -- computes the tail/recession cone of a polyhedron
- toSublattice -- calculates the preimage of a polytope in the sublattice generated by its lattice points
- triangulate -- computes a triangulation of a polytope
- vertexEdgeMatrix -- computes the vertex-edge-relations matrix
- vertexFacetMatrix -- computes the vertex-facet-relations matrix
- vertices -- displays the vertices of a Polyhedron or a PolyhedralComplex
- volume -- computes the volume of a polytope
- Working with cones
- Working with fans
- Working with fans - Part 2
- Working with polyhedra