  We construct the hyperkahler cones corresponding to the Quaternion-Kahler
orthogonal Wolf spaces SO(n+4)/(SO(n)xSO(4)) and their non-compact versions,
which appear in hypermultiplet couplings to N=2 supergravity. The geometry is
completely encoded by a single function, the hyperkahler potential, which we
compute from an SU(2) hyperkahler quotient of flat space. We derive the Killing
vectors and moment maps for the SO(n+4) isometry group on the hyperkahler cone.
For the non-compact case, the isometry group SO(n,4) contains n+2 abelian
isometries which can be used to find a dual description in terms of n tensor
multiplets and one double-tensor multiplet. Finally, using a representation of
the hyperkahler quotient via quiver diagrams, we deduce the existence of a new
eight dimensional ALE space.
