Two Families of Unravelled Abstract Regular Polytopes in Bn
Robert Nicolaides, Peter Rowley
TL;DR
This paper introduces two new families of unravelled abstract regular polytopes within Coxeter groups of type Bn, expanding the understanding of their structure with one family of fixed rank 4 and another with arbitrarily large rank.
Contribution
It presents the first known examples of unravelled abstract regular polytopes in Coxeter groups of type Bn, including a family with unbounded rank.
Findings
Two families of unravelled abstract regular polytopes are constructed.
One family has rank 4, the other has arbitrarily large rank.
The work broadens the classification of regular polytopes in Coxeter groups.
Abstract
This paper exhibits two families of unravelled abstract regular polytopes in Coxeter groups of type Bn. For one family they have rank 4 while the other family has arbitrarily large rank.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Finite Group Theory Research