A Hyperbolic Surface With A Square Grid Net
  We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage of the extended real line under the projection map is homeomorphic to the square grid in the plane. This answers a question raised by \`E. B. Vinberg. 
Lukas Geyer and Sergei Merenkov