We consider the question of when an unorientable surface without boundary can be tiled by an (l,m,n) triangle. We require that the the tiling have a "substantial" automorphism group, giving a highly symmetric triangulation of the surface. We use the well known theory and classication of low genus, quasiplatonic surfaces and symmetries of Riemann surfaces to outline a classification algorithm that only uses nite group calculations. We report progress on carrying out this program for low genus surfaces and present some examples of families of such surfaces.

The triangulations of the surfaces can be used to aid quantum coding theory. We discuss this application briefly

though the major focus is on the tilings.