  The number of Lame equations with finite (ordinary or projective) monodromy
has been conjectured by S. R. Dahmen, and a few proofs have been proposed. It
is known that Lame equations with unitary monodromy are corresponding to
spherical tori with one conical singularity, and the geometry of such surfaces
had been studied with triangulation recently. In this paper, we will apply the
results on spherical tori to give an alternative proof of Dahmen's conjectures.
