Construction of chiral 4-polytopes with alternating or symmetric automorphism group
In this paper we describe a construction for finite abstract chiral 4-polytopes with Schlfli type \(\{3,3,k\}\) (with tetrahedral facets) and with an alternating or symmetric group as automorphism group. We use it to prove that for all but finitely many \(n\), both \(A_n\) and \(S_n\) are the automorphism groups of such a polytope. We also show that the vertex-figures of the polytopes obtained from our construction are chiral.
symmetric groups abstract polytopes chiral polytopes alternating groups