Chamfering operation on k-orbit maps

Abstract

A map, as a 2-cell embedding of a graph on a closed surface, is called a k-orbit map if the group of automorphisms (or symmetries) of the map partitions its set of flags into k orbits. Orbanić, Pellicer and Weiss studied the effects of operations as medial and truncation on k-orbit maps. In this paper we study the possible symmetry types of maps that result from other maps after applying the chamfering operation and we give the number of possible flag-orbits that has the chamfering map of a k-orbit map, even if we repeat this operation t times.