Toric selfdual Einstein metrics on compact orbifolds

We prove that any compact selfdual Einstein 4-orbifold of positive scalar curvature whose isometry group contains a 2-torus is, up to an orbifold covering, a quaternion Kaehler quotient of (k-1)-dimensional quaternionic projective space by a (k-2)-torus for some $k\ge 2$. We also obtain a topological classification in terms of the intersection form of the 4-orbifold.