2022/08/01 by Isabel Hubard, Hubard, Isabel, Elías Mochán +1 · 1 citation
Computer Science · Mathematics · #05E18 (Primary) 06A11 (Secondary) #51A10 #52B15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2208.00547
openalex publication_date 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract polytopes generalize the classical notion of convex polytopes to more general combinatorial structures. The most studied ones are regular and chiral polytopes, as it is well-known, they can be constructed as coset geometries from their automorphism groups. This is also known to be true for 2- and 3- orbit 3-polytopes. In this paper we show that every abstract n-polytope can be constructed as a coset geometry. This construction is done by giving a characterization, in terms of generators, relations and intersection conditions, of the automorphism group of a k-orbit polytope with given symmetry type graph. Furthermore, we use these results to show that for all k≠ 2, there exist k-orbit n-polytopes with Boolean automorphism groups, for all n≥ 3.