3 papers
math.GR2021
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…
math.GR2021
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 $\SL_3(q)$,…
math.GR2021
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…