Abstract. For $k\geq7$, we determine the minimal area of a compact hyperbolic surface, and an oriented compact hyperbolic surface that can be tiled by embedded regular triangles of angle $2\pi /k$. Based on this, all the cases of equality in László Fejes Tóth's triangle bound for hyperbolic surfaces are described.

AMS Subject Classification (1991): 51M10, 52C22

Keyword(s): tiling of hyperbolic surfaces

Received April 14, 2010, and in revised form January 11, 2011. (Registered under 28/2010.)