It has recently been shown that a stationary, asymptotically flat vacuum
black hole in five space-time dimensions with two commuting axial symmetries
must have an event horizon with either a spherical, ring or lens-space
topology. In this paper, we study the third possibility, a so-called black lens
with L(n,1) horizon topology. Using the inverse scattering method, we construct
a black lens solution with the simplest possible rod structure, and possessing
a single asymptotic angular momentum. Its properties are then analysed; in
particular, it is shown that there must either be a conical singularity or a
naked curvature singularity present in the space-time.Comment: 25 pages, 2 figures, LaTe