Unravelled abstract regular polytopes

This paper introduces the notion of an unravelled abstract regular polytope, and proves that ${SL}_{3} (q) ⋊ ⟨ t ⟩$ , where $t$ is the transpose inverse automorphism of ${SL}_{3} (q)$ , possesses such polytopes for various congruences of $q$ . A large number of small examples of such polytopes are given, along with extensive details of their various properties.

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Keywords

abstract regular polytopes, unravelled

Mathematical Subject Classification

Primary: 52B05

Secondary: 20H30

Milestones

Received: 16 January 2024

Revised: 18 August 2024

Accepted: 13 September 2024

Published: 22 October 2024

Authors

Robert Nicolaides
Department of Mathematics Manchester University Manchester United Kingdom

Peter Rowley
Department of Mathematics Manchester University Manchester United Kingdom

Vol. 21, No. 2, 2024

Robert Nicolaides and Peter Rowley

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors