Branched cyclic regular coverings over platonic maps

作者：Hu, Kan^*; Nedela, Roman; Wang, Na-Er

来源：European Journal of Combinatorics, 2014, 36: 531-549.

DOI：10.1016/j.ejc.2013.09.006

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 Jones and Surowski [G.A. Jones, D.B. Surowski, Cyclic regular coverings of the Platonic maps, European J. Combin. 21 (2000) 333-345] classifying the cyclic regular coverings over platonic maps with branched points exclusively at vertices, or at face-centres.

• 出版日期2014-2
• 单位浙江海洋大学