2013/03/27 by Gabe Cunningham, Maria del Rio Francos, Cunningham, Gabe +6
Engineering · Mathematics · #51M20 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Primary 52B15 #Secondary 05C25 #graph theory and CDMA systems #math.CO #msc:05C25 #msc:51M20 #msc:52B15
paper · pdf · doi:10.48550/arxiv.1303.6802
openalex publication_date 2013/03/27 · arxiv created 2013/06/07 · arxiv updated 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A k-orbit maniplex is one that has k orbits of flags under the action of its automorphism group. In this paper we extend the notion of symmetry type graphs of maps to that of maniplexes and polytopes and make use of them to study k-orbit maniplexes, as well as fully-transitive 3-maniplexes. In particular, we show that there are no fully-transtive k-orbit 3-mainplexes with k > 1 an odd number, we classify 3-orbit mainplexes and determine all face transitivities for 3- and 4-orbit maniplexes. Moreover, we give generators of the automorphism group of a polytope or a maniplex, given its symmetry type graph. Finally, we extend these notions to oriented polytopes, in particular we classify oriented 2-orbit maniplexes and give generators for their orientation preserving automorphism group.