Computing convex hulls and counting integer points with polymake

TL;DR

This paper reviews current methods and algorithms for computing convex hulls, integer hulls, and counting lattice points in convex polytopes using polymake, providing practical insights and rules of thumb.

Contribution

It offers a comprehensive overview of algorithms and implementations for convex hulls and lattice point counting within the polymake system, including practical guidelines.

Findings

Summarizes ten practical rules of thumb for computing integer hulls.

Evaluates various algorithms and their performance within polymake.

Provides insights into the state-of-the-art computational techniques.

Abstract

The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and implementations. Our experience in this area is summarized in ten "rules of thumb".