Equality in Laszlo Fejes Toth's triangle bound for hyperbolic surfaces
  For k>6, 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 Laszlo Fejes Toth's triangle bound for hyperbolic surfaces are described. 
C. Barvard, K. J. Boroczky, B. Ormos, I. Prok, L. Vena, G. Wintsche
math.DG