  On an affine flat manifold with coordinates x^j and convex local potential
function f, we call the affine Kahler metric f_{ij} dx^i dx^j semi-flat
Calabi-Yau if it satisfies det f_{ij} = 1. Recently Gross-Wilson have
constructed many such metrics on S^2 minus 24 singularities, as degenerate
limits of Calabi-Yau metrics on elliptic K3 surfaces. We construct many more
such metrics on S^2, singular at any 6 or more points, and compute the local
affine structure near the singularities. The techniques involve affine
differential geometry and solving a semilinear PDE on S^2 minus singularities.
We also compute the action mirror symmetry should have on the resulting
surfaces.
