In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely automorphisms, where g is the genus of the surface. This number is maximal by virtue of Hurwitz`s theorem on automorphisms {Harv|Hurwitz|1893}. They are also referred to as Hurwitz curves, interpreting them ....