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

The modular group $\mathrm{\Gamma }$ (which is the Hecke group $H_3$) can be used to study triangular maps. Here we use the Hecke group $H_4$ 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.