Elementary abelian regular coverings of Platonic maps, Case I: ordinary representations

Details Elementary abelian regular coverings of Platonic maps, Case I: ordinary representations Elementary abelian regular coverings of Platonic maps, Case I: ordinary representations

2012-01-25

arxiv.org/abs/1201.5245v1

Mathematics

Combinatorics

25 pages

Scientific paper

We classify the orientably regular maps which are elementary abelian regular branched coverings of Platonic maps M, in the case where the covering group and the rotation group G of M have coprime orders. The method involves studying the representations of G on certain homology groups of the sphere, punctured at the branch-points. We give a complete classification for branching over faces (or, dually, vertices) of M, and outline how the method extends to other branching patterns.

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