  We present the general solution to the Plebanski equation for an H-space that
admits Killing vectors for an entire SU(2) of symmetries, which is therefore
also the general solution of the sDiff(2)Toda equation that allows these
symmetries. Desiring these solutions as a bridge toward the future for yet more
general solutions of the sDiff(2)Toda equation, we generalize the earlier work
of Olivier, on the Atiyah-Hitchin metric, and re-formulate work of Babich and
Korotkin, and Tod, on the Bianchi IX approach to a metric with an SU(2) of
symmetries. We also give careful delineations of the conformal transformations
required to ensure that a metric of Bianchi IX type has zero Ricci tensor, so
that it is a self-dual, vacuum solution of the complex-valued version of
Einstein's equations, as appropriate for the original Plebanski equation.
