Conder, Marston; Hubard, Isabel; O'Reilly-Regueiro, Eugenia; Pellicer, Daniel

Construction of chiral 4-polytopes with alternating or symmetric automorphism group

J. Algebr. Comb. 42(1), 225-244 (2015)
DOI: 10.1007/s10801-014-0579-5


In this paper we describe a construction for finite abstract chiral 4-polytopes with Schläfli 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.

Mathematics Subject Classification

51M20, 20B30


abstract polytopes, chiral polytopes, symmetric groups, alternating groups