OldPolyhedra -- for computations with convex polyhedra, cones, and fans
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affineHull -- computes the affine hull of a polyhedron
affineImage -- computes the affine image of a cone or polyhedron
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affinePreimage -- computes the affine preimage of a cone or polyhedron
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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
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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
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cones -- computes all cones of a fan of a certain dimension
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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
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directProduct -- computes the direct product of two convex objects
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dualCayley (missing documentation)
dualCayleyFace (missing documentation)
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ehrhart -- calculates the Ehrhart polynomial of a polytope
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faceFan -- computes the fan generated by the cones over the faces
faceLattice -- computes the face lattice of a cone or polyhedron
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faceOf (missing documentation)
faces -- computes all faces of a certain codimension of a Cone or Polyhedron
Fan -- the class of all fans
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fVector -- computes the f-vector of a Cone or Polyhedron
halfspaces -- computes the defining half-spaces of a Cone or a Polyhedron
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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
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inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron
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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
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isPointed -- checks if a Cone or Fan is pointed
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isPure -- checks if a Fan or PolyhedralComplex is of pure dimension
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isSmooth -- checks if a Cone or Fan is smooth
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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
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normalFan -- computes the normalFan of a polyhedron
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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
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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
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rays -- displays all rays of a Cone, a Fan, or a Polyhedron
saveSession -- save the actual Polyhedra session to a file
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skeleton -- computes the k-skeleton of a Fan or PolyhedralComplex
smallestFace -- determines the smallest face of the Cone/Polyhedron containing a point
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statePolytope -- computes the state polytope of a homogeneous ideal
stdSimplex -- generates the d-dimensional standard simplex
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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
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vertices -- displays the vertices of a Polyhedron or a PolyhedralComplex
volume -- computes the volume of a polytope
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