Hypermaps and multiply quasiplatonic Riemann surfaces
  Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases with isomorphic automorphism groups. 
Gareth A. Jones
math.CO math.GR