Chiral Hypermaps of Small Genus

A hypermap H is a cellular embedding of a 3-valent graph G into a closed surface which cells are 3-coloured (adjacent cells have dierent colours). The vertices of G are called flags of H and let us denote by F the set of flags. An automorphism of the underlying graph which extends to a colour preserving self-homeomorphism of the surface is called an automorphism of the hypermap. If the surface is orientable the automorphisms of H split into two classes, orientation preserving and orientation reversing automorphisms. It is not dicult to observe that |Aut(H)| | F| while for the group of orientation preserving automorphisms