Medial symmetry type graphs [article]

Isabel Hubard, Alen Orbanić, Tomaž Pisanski, María del Río Francos
2013 arXiv   pre-print
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 Orbanić, Pellicer and Weiss, for k ≤ 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≤ 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.
arXiv:1301.7637v1 fatcat:ao62f72byfhkxaz6cjewmdmwnq