# 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¶

### Polyhedral complexes¶

### Toric geometry¶

### Base classes for polyhedra¶

### Backends for Polyhedra¶

- The cdd backend for polyhedral computations
- The Python backend
- 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