  We apply the twistor construction for higher-dimensional black holes to known
examples in five space-time dimensions. First the patching matrices are
calculated from the explicit metric for these examples. Then an ansatz is
proposed for obtaining the patching matrix instead from the data of rod
structure and angular momenta. The ansatz is tested on examples with up to
three nuts, and these are shown to give flat space, the Myers-Perry solution
and the black ring, as expected. Rules for the transition between different
adaptations of the patching matrix and for the elimination of conical
singularities are developed and seen to work.
