4 papers
A Note on the Rank 5 Polytopes of M24
Veronica Kelsey, Robert Nicolaides, Peter Rowley
The maximal rank of an abstract regular polytope for M24, the Mathieu group of degree 24, is 5. There are four such polytopes of rank 5 and in this note we describe them using Curt…
Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups
Robert Nicolaides, Peter Rowley
Two new Elnitsky tilings for Coxeter groups of type are displayed as certain subtilings. Additionally, a new tiling for the non-crystallographic Coxeter group of type…
Unravelled Abstract Regular Polytopes
Robert Nicolaides, Peter Rowley
This paper introduces the notion of an unravelled abstract regular polytope, and proves that $\SL_3(q) \rtimes <t>$, where is the transpose inverse automorphism of $\SL_3(q)$,…
Two Families of Unravelled Abstract Regular Polytopes in Bn
Robert Nicolaides, Peter Rowley
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…