  It is well known that any 4-dimensional hyperkahler metric with two commuting
Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from
a harmonic function invariant under a Killing field on R^3. In this paper, we
find all selfdual Einstein metrics of nonzero scalar curvature with two
commuting Killing fields. They are given explicitly in terms of a local
eigenfunction of the Laplacian on the hyperbolic plane. We discuss the relation
of this construction to a class of selfdual spaces found by Joyce, and some
Einstein-Weyl spaces found by Ward, and then show that certain `multipole'
hyperbolic eigenfunctions yield explicit formulae for the quaternion-kahler
quotients of HP(m-1) by an (m-2)-torus first studied by Galicki and Lawson. As
a consequence we are able to place the well-known cohomogeneity one metrics,
the quaternion-kahler quotients of HP(2) (and noncompact analogues), and the
more recently studied selfdual Einstein hermitian metrics in a unified
framework, and give new complete examples.
