# Combinatorial and Discrete Geometry#

Sage includes classes for hyperplane arrangements, polyhedra, toric varieties (including polyhedral cones and fans), triangulations and some other helper classes and functions.

## Hyperplane arrangements#

## Polyhedral computations#

### Polyhedra#

- Library of commonly used, famous, or interesting polytopes
- Polyhedra
- Parents for Polyhedra
- H(yperplane) and V(ertex) representation objects for polyhedra
- Functions for plotting polyhedra
- A class to keep information about faces of a polyhedron
- Generate cdd
`.ext`

/`.ine`

file format - Formal modules generated by polyhedra

### Lattice polyhedra#

### Combinatorial Polyhedra#

### Polyhedral complexes#

### Toric geometry#

### Base classes for polyhedra#

- Base class for polyhedra: Initialization and access to Vrepresentation and Hrepresentation
- Base class for polyhedra: Implementation of the
`ConvexSet_base`

API - Base class for polyhedra: Methods related to lattice points
- Base class for polyhedra: Methods regarding the combinatorics of a polyhedron
- Base class for polyhedra: Graph-theoretic methods
- Base class for polyhedra: Methods for constructing new polyhedra
- Base class for polyhedra: Methods for plotting and affine hull projection
- Base class for polyhedra: Methods for triangulation and volume computation
- Base class for polyhedra: Miscellaneous methods
- Base class for polyhedra over \(\QQ\)
- Base class for polyhedra over \(\ZZ\)
- Base class for polyhedra over
`RDF`

### Backends for Polyhedra#

- The cdd backend for polyhedral computations
- The cdd backend for polyhedral computations, floating point version
- The Python backend
- The Python backend, using number fields internally
- The Normaliz backend for polyhedral computations
- The polymake backend for polyhedral computations
- The PPL (Parma Polyhedra Library) backend for polyhedral computations
- Double Description Algorithm for Cones
- Double Description for Arbitrary Polyhedra