Karabáš, Ján, 1977-

Archimedean maps of higher genera / Ján Karabáš, Roman Nedela. -- The paper focuses on the classification of vertex-transitive polyhedral maps of genus from 2 to 4. These maps naturally generalise the spherical maps associated with the classical Archimedean solids. Our analysis is based on the fact that each Archimedean map on an orientable surface projects onto a one- or a two-vertex quotient map. For a given genus g>= 2 the number of quotients to consider is bounded by a function of g. All Archimedean maps of genus g can be reconstructed from these quotients as regular covers with covering transformation group isomorphic to a group G from a set of g-admissible groups. Since the lists of groups acting on surfaces of genus 2,3, and 4 are known, the problem can be solved by a computer-aided case-to-case analysis

In Mathematics of Computation. -- Providence : American Mathematical Society, 2012. -- ISSN 0025-5718. -- ISSN 1088-6842. -- Vol. 81, no. 277 (2012), pp. 569-583