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# 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
- A class to keep information about faces of a polyhedron
- Generate cdd `.ext` / `.ine` file format
- Pseudolines
- Triangulations of a point configuration
- Base classes for triangulations
- A triangulation
- Hyperplane Arrangements
- Library of Hyperplane Arrangements
- Hyperplanes
- Affine Subspaces of a Vector Space
- Linear Expressions

## Backends for Polyhedral Computations

- The cdd backend for polyhedral computations
- The PPL (Parma Polyhedra Library) backend for polyhedral computations
- The Python backend
- Double Description Algorithm for Cones
- Double Description for Arbitrary Polyhedra
- Base class for polyhedra
- Base class for polyhedra over \(\QQ\)
- Base class for polyhedra over \(\ZZ\)
- Base class for polyhedra over `RDF`.

# Indices and Tables

- Index
- Module Index
- Search Page

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