A Note on the Rank 5 Polytopes of M24

Veronica Kelsey, Robert Nicolaides, Peter Rowley

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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. This description is then used to give an upper bound for the diameter of the chamber graphs of these polytopes.
Original languageEnglish
JournalInnovations in Incidence Geometry: Algebraic, Topological and Combinatoria
Publication statusAccepted/In press - 30 Nov 2023


  • abstract regular polytope
  • maximal rank
  • Mathieu group
  • MOG


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