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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

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.

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