SELF-DUAL REGULAR MAPS FROM MEDIAL GRAPHS
Dan Archdeacon · 1992
this paper we investigate the relationship between the symmetries of a map and those of its medial map. The main issue of this study is a theorem saying that a map M (orientable or not) is regular and self-dual if and only if the medial map m(M ) is regular. This theorem combined with a lifting technique based on special voltage assignments allows us to construct new oriented regular self-dual maps from old ones. As a consequence, we obtain that if G is a d-valent graph admitting an oriented regular self-dual map, then the graph G