On the rank of Suzuki polytopes: an answer to Hubard and Leemans

Abstract

In this paper we show that the rank of every chiral polytope having a Suzuki group as automorphism group is 3. This gives a positive answer to a conjecture of Isabel Hubard and Dimitri Leemans.2010 Mathematics Subject Classification. 52B11, 20D06. Key words and phrases. abstract chiral polytopes, Suzuki simple groups. 1 I first heard about this conjecture in the lovely 2014 summer course in algebraic graph theory by Dimitri Leemans in Rogla, Slovenia. Here I express my gratitude to Dimitri for such a wonderful series of lectures and to the organizers of the Rogla Summer School.