Abstract
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 Schläfli 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 Schläfli symbol of P is arbitrarily large.
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