  For each sphere with three orbifold points, we construct an algorithm to
compute the open Gromov-Witten potential, which serves as the quantum-corrected
Landau-Ginzburg mirror and is an infinite series in general. This gives the
first class of general-type geometries whose full potentials can be computed.
As a consequence we obtain an enumerative meaning of mirror maps for elliptic
curve quotients. Furthermore, we prove that the open Gromov-Witten potential is
convergent, even in the general-type cases, and has an isolated singularity at
the origin, which is an important ingredient of proving homological mirror
symmetry.
