Isomorphisms of Cayley graphs of surface groups - Bozejko, M.; Dykema, K.; Lehner, F. (Algebra and Discrete Mathematics, 2006)
A combinatorial proof is given for the fact that the Cayley graph of the fundamental group Γg of the closed, orientable surface of genus g ≥ 2 with respect to the usual generating set is isomorphic to the Cayley graph of a certain Coxeter group generated by 4g elements.