Construction of infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes and their growth rates

TL;DR

This paper constructs infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes with Perron number growth rates, providing the first example of such non-compact infinite polytopal series.

Contribution

It introduces the first known infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes with Perron number growth rates.

Findings

Constructed infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes

Established that their growth rates are Perron numbers

First example of non-compact infinite polytopal series

Abstract

We construct infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes whose growth rates are Perron numbers. This infinite series is the first example of such a non-compact infinite polytopal series.