  A spherical n-gon is a bordered surface homeomorphic to a closed disk, with n
distinguished boundary points called corners, equipped with a Riemannian metric
of constant curvature 1, except at the corners, and such that the boundary arcs
between the corners are geodesic. We discuss the problem of classification of
these polygons and enumerate them in the case that two angles at the corners
are not multiples of pi. The problem is equivalent to classification of some
second order linear differential equations with regular singularities, with
real parameters and unitary monodromy.
