  We present a four-dimensional double-black-hole (or dihole) solution in
Kaluza-Klein theory, describing a superposition of an electrically charged and
a magnetically charged black hole. This system can be balanced for
appropriately chosen parameters, and the resulting space-time is completely
regular on and outside the event horizons. This solution was constructed using
the inverse-scattering method in five-dimensional vacuum gravity, in which it
describes a rotating black ring surrounding a static black hole on a Taub-NUT
background space. Various properties of this solution are studied, from both a
four- and five-dimensional perspective.
