Branched cyclic regular coverings over Platonic maps. (English) Zbl 1284.05215
Summary: A map is a 2-cell decomposition of a closed surface. A map on an orientable surface is called regular if its group of orientation-preserving automorphisms acts transitively on the set of darts (edges endowed with an orientation). In this paper we investigate regular maps which are regular covers over Platonic maps with a cyclic group of covering transformations. We describe all such maps in terms of parametrised group presentations. This generalises the work of G. A. Jones and D. B. Surowski [Eur. J. Comb. 21, No. 3, 407–418 (2000; Zbl 0946.05067)] classifying the cyclic regular coverings over Platonic maps with branched points exclusively at vertices, or at face-centres.
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
Citations:
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