Realization of Regular Maps of Large Genus

  • Faniry RazafindrazakaEmail author
  • Konrad Polthier
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Regular maps are an algebraic concept to describe most symmetric tilings of closed surfaces of arbitrary genus. All such regular maps resp. symmetric tilings of surfaces up to genus 302 are algebraically known in the form of symmetry groups acting on their universal covering space. But still little is known about geometric realizations, i.e. about finding most symmetric embeddings of closed surfaces with high genus and a supported most symmetric tiling. In this report, we will construct some new highly symmetric embeddings of regular maps of up to genus 61 and thereby shed some new light on this fundamental problem at the interface of algebra, differential geometry, and topology.


Symmetry Group Hyperbolic Space Fundamental Domain Hyperbolic Plane Edge Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Jack van Wijk for material support. This research was supported by the DFG-Collaborative Research Center, TRR109, “Discretization in Geometry and Dynamics”.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Freie Universität BerlinBerlinGermany

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