  Using a generalized Weyl formalism, we show how stationary, axisymmetric
solutions of the four-dimensional vacuum Einstein equation can be turned into
static, axisymmetric solutions of five-dimensional dilaton gravity coupled to a
two-form gauge field. This procedure is then used to obtain new solutions of
the latter theory describing pairs of extremal magnetic black holes with
opposite charges, known as black diholes. These diholes are kept in static
equilibrium by membrane-like conical singularities stretching along two
different directions. We also present solutions describing diholes suspended in
a background magnetic field, and with unbalanced charges.
