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On the rank $5$ polytopes of the Higman–Sims simple group

Veronica Kelsey, Robert Nicolaides and Peter Rowley

Vol. 19 (2022), No. 4, 153–164
Abstract

The maximal rank of an abstract regular polytope for the Higman–Sims simple group is 5. There are four such polytopes of rank 5 and in this note we describe them using the Higman–Sims graph and the decomposition of this graph into five double covers of the Petersen graph.

Keywords
polytopes, C-strings, Higman–Sims simple group
Mathematical Subject Classification
Primary: 52B15
Secondary: 20D08
Milestones
Received: 10 January 2022
Revised: 23 May 2022
Accepted: 7 August 2022
Published: 1 December 2022
Authors
Veronica Kelsey
Department of Mathematics
University of Manchester
Manchester
United Kingdom
Robert Nicolaides
Department of Mathematics
University of Manchester
Manchester
United Kingdom
Peter Rowley
Department of Mathematics
University of Manchester
Manchester
United Kingdom