  Using the inverse scattering method to solve the five-dimensional vacuum
Einstein equations, we construct an asymptotically flat four-soliton solution
as a stationary and bi-axisymmetric solution. We impose certain boundary
conditions on this solution so that it includes a rotating black hole whose
horizon-cross section is topologically a lens space of L(2,1). The solution has
nine parameters but three only is physically independent due to the constraint
equations. The remaining degrees of freedom correspond to the mass and two
independent angular momenta of the black hole. We analyze a few simple cases in
detail, in particular, the static case with two zero-angular momenta and the
stationary case with a single non-zero angular momentum.
