par Fernandes, Maria Elisa;Leemans, Dimitri ;Mixer, Mark
Référence Transactions of the American Mathematical Society, 370, 12, page (8833-8857)
Publication Publié, 2018-12-01
Article révisé par les pairs
Résumé : Up to isomorphism and duality, there are exactly two nondegener-ate abstract regular polytopes of rank greater than n−3 (one of rank n−1 and one of rank n − 2) with automorphism groups that are transitive permutation groups of degree n ≥ 7. In this paper we extend this classification of high rank regular polytopes to include the ranks n − 3 and n − 4. The result is, up to isomorphism and duality, there are exactly seven abstract regular polytopes of rank n − 3 for each n ≥ 9, and there are nine abstract regular polytopes of rank n−4 for each n ≥ 11. Moreover, we show that if a transitive permutation group Γ of degree n ≥ 11 is the automorphism group of an abstract regular polytope of rank at least n − 4, then Γ =∼ S n .