On the Schläfli symbol of chiral extensions of polytopes

Given an abstract n-polytope K , an abstract ( n + 1 ) -polytope P is an extension of K if all the facets of P are isomorphic to K . A chiral polytope is a polytope with maximal rotational symmetry that does not admit any reflections. If P is a chiral extension of K , then all but the last entry of the Schlafli symbol of P are determined. In this paper we introduce some constructions of chiral extensions P of certain chiral polytopes in such a way that the last entry of the Schlafli symbol of P is arbitrarily large.