  Using a ramified cover of the two-sphere by the torus, we prove a local
optimal inequality between the diastole and the area on the two-sphere near a
singular metric. This singular metric, made of two equilateral triangles glued
along their boundary, has been conjectured by E. Calabi to achieve the best
ratio area over the square of the length of a shortest closed geodesic. Our
diastolic inequality asserts that this conjecture is to some extent locally
true.
