Platonic Solids and High Genus Covers of Lattice Surfaces

@article{Athreya2020PlatonicSA,
  title={Platonic Solids and High Genus Covers of Lattice Surfaces},
  author={Jayadev S. Athreya and David Aulicino and William P. Hooper},
  journal={Experimental Mathematics},
  year={2020}
}
We study the translation surfaces obtained by considering the unfoldings of the surfaces of Platonic solids. We show that they are all lattice surfaces and we compute the topology of the associated Teichmuller curves. Using an algorithm that can be used generally to compute Teichmuller curves of translation covers of primitive lattice surfaces, we show that the Teichmuller curve of the unfolded dodecahedron has genus 131 with 19 cone singularities and 362 cusps. We provide both theoretical and… 
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