Drawing polytopal graphs with polymake

TL;DR

This paper explains how to generate meaningful visual representations of complex geometric objects like convex polytopes and tropical polytopes using the polymake software, addressing graph drawing challenges in geometric combinatorics.

Contribution

It introduces methods implemented in polymake for visualizing high-dimensional geometric objects and related graph drawing problems in geometric combinatorics.

Findings

Effective visualization techniques for convex polytopes and tropical objects.

Implementation of methods in the polymake software system.

Application to high-dimensional geometric structures.

Abstract

This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight spans of finite metric spaces and tropical polytopes. In all our cases we arrive at specific, geometrically motivated, graph drawing problems. The methods displayed are implemented in the software system polymake.