Hecke-Farey coordinates for Bring's curve that gives Bring's surface

Abstract

The modular group (which is the Hecke group H3) can be used to study triangular maps. Here we use the Hecke group H4 to study the regular map that underlies Bring's surface of genus 4. Our main result is the determination of the 20-sided hyperbolic polygon that gives Bring's surface.

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