Medial symmetry type graphs
Summary: A \(k\)-orbit map is a map with its automorphism group partitioning the set of flags into \(k\) orbits. Recently \(k\)-orbit maps were studied by \textit{A. Orbanić} et al. [J. Comb. Theory, Ser. A 117, No. 4, 411--429 (2010; Zbl 1197.51005)], for \(k \leq 4\). In this paper we use symmetry type graphs to extend such study and classify all the types of 5-orbit maps, as well as all self-dual, properly and improperly, symmetry type of \(k\)-orbit maps with \(k\leq 7\). Moreover, we determine, for small values of \(k\), all types of \(k\)-orbits maps that are medial maps. Self-dualities constitute an important tool in this quest.
scientific article; zbMATH DE number 6330301
scientific article