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A note on the rank 5 polytopes of M$_{24}$

Veronica Kelsey, Robert Nicolaides and Peter Rowley

Vol. 21 (2024), No. 1, 11–15
DOI: 10.2140/iig.2024.21.11
Abstract

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 Curtis’s MOG.

Keywords
abstract regular polytope, maximal rank, Mathieu group, MOG
Mathematical Subject Classification
Primary: 52B15
Secondary: 20D08
Milestones
Received: 1 August 2023
Revised: 27 September 2023
Accepted: 29 October 2023
Published: 9 January 2024
Authors
Veronica Kelsey
Department of Mathematics
University of Manchester
Manchester
United Kingdom
Robert Nicolaides
Department of Mathematics
Manchester University
Manchester
United Kingdom
Peter Rowley
School of Mathematics
Manchester University
Manchester
United Kingdom