Studying Wythoff and Zometool Constructions using Maple

TL;DR

This paper introduces a Maple software package that facilitates the analysis and construction of polyhedral structures, including Zometool constructibility, Wythoff constructions, and Coxeter plane projections, aiding researchers in geometric and combinatorial studies.

Contribution

The paper presents a novel Maple package that integrates multiple tools for polyhedral analysis, including constructibility checks, structure manipulation, and visualization of Wythoff and Coxeter constructions.

Findings

Efficient computation of Zometool constructibility.

Ability to manipulate and visualize Zometool structures.

Generation of examples via Wythoff construction and Coxeter plane projections.

Abstract

We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to determine how to best build a given structure. Third, the package allows for an easy computation of the polytopes obtained by the kaleiodoscopic construction called the Wythoff construction. This feature provides a source of multiple examples. Fourth, the package allows the projection on Coxeter planes