Bicontactual Regular Hypermaps

Bicontactual regular maps (regular maps with the property that each face meets only two others) were introduced and classified by Wilson in 1985. This property generalizes to hypermaps (cellular embeddings of hypergraphs in compact surfaces) giving rise to three types of bicontactuality, namely, the edge-twin, the vertex-twin, and the alternate (the first two of which are the dual of each other). In 2003 Wilson and Breda classified (up to an isomorphism and duality) the bicontactual regular nonorientable hypermaps, leaving the orientable case open. In this paper we classify the bicontactual regular oriented hypermaps. [PUBLICATION ABSTRACT]