Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1090/S0025-5718-2011-02502-0 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Polyhedron,Archimedean solid,map,surface,group,graph embedding | Archimedean solid,Semiregular polyhedron,Combinatorics,Graph embedding,Polyhedron,Mathematics | Journal |
Volume | Issue | ISSN |
81 | 277 | 0025-5718 |
Citations | PageRank | References |
0 | 0.34 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| JáN Karabáš | 1 | 3 | 2.19 |
| Roman Nedela | 2 | 392 | 47.78 |