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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.

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