Combinatorial Geometry

Sage includes classes for convex rational polyhedral cones and fans, Groebner fans, lattice and reflexive polytopes (with integral coordinates), and generic polytopes and polyhedra (with rational or numerical coordinates).

• Toric lattices
• Convex rational polyhedral cones
• Rational polyhedral fans
• Morphisms between toric lattices compatible with fans
• Point collections
• Toric plotter
• Groebner Fans
• Lattice and reflexive polytopes
• Polyhedra
• H(yperplane) and V(ertex) representation objects for polyhedra
• Library of commonly used, famous, or interesting polytopes
• Functions for plotting polyhedra
• Base class for polyhedra
• Base class for polyhedra over
• Base class for polyhedra over RDF.
• The cdd backend for polyhedral computations
• The PPL (Parma Polyhedra Library) backend for polyhedral computations
• Generate cdd .ext / .ine file format
• Triangulations of a point configuration
• Base classes for triangulations
• A triangulation