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Unravelled abstract regular polytopes

Robert Nicolaides and Peter Rowley

Vol. 21 (2024), No. 2, 139–160
Abstract

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.

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