  The correspondence of stationary, axisymmetric, asymptotically flat
space-times and bundles over a reduced twistor space has been established in
four dimensions. The main impediment for an application of this correspondence
to examples in higher dimensions is the lack of a higher-dimensional equivalent
of the Ernst potential. This thesis will propose such a generalized Ernst
potential, point out where the rod structure of the space-time can be found in
the twistor picture and thereby provide a procedure for generating solutions to
the Einstein field equations in higher dimensions from the rod structure, other
asymptotic data, and the requirement of a regular axis. Examples in five
dimensions are studied and necessary tools are developed, in particular rules
for the transition between different adaptations of the patching matrix and
rules for the elimination of conical singularities.
