Finite Polytopes have Finite Regular Covers
B. Monson, Egon Schulte
TL;DR
This paper proves that every finite abstract n-polytope can be covered by a finite regular n-polytope, establishing a significant connection between finite polytopes and their regular covers.
Contribution
It introduces a universal covering result for finite abstract polytopes, showing they all have finite regular covers, which was previously unknown.
Findings
Every finite abstract n-polytope has a finite regular cover.
The result applies to all finite abstract polytopes regardless of their symmetry.
This bridges the gap between finite polytopes and regular polytopes in a new way.
Abstract
We prove that any finite, abstract n-polytope is covered by a finite, abstract regular n-polytope.
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Taxonomy
TopicsOptimization and Packing Problems · semigroups and automata theory · Advanced Graph Theory Research