Vertex-transitive maps with Schlafli type {3,7}

Among all equivelar vertex-transitive maps on a given closed surface S, the automorphism groups of maps with Schlafli types {3, 7} and {7, 3} allow the highest possible order. We describe a procedure to transform all such maps into 1- or 2-orbit maps, whose symmetry type has been previously studied. In doing so we provide two procedures to find vertextransitive maps with Schlafli type {3, 7} which are neither regular nor chiral. One of them is by means of operations while the other consists of interpreting them as generalized Cayley maps. We determine all such maps on surfaces with Euler characteristic -1 >= chi >= 40. (C) 2013 Published by Elsevier B.V.