  We introduce an efficient configuration space technique which allows one to
compute a class of Feynman diagrams which generalize the scalar sunset topology
to any number of massive internal lines. General tensor vertex structures and
modifications of the propagators due to particle emission with vanishing
momenta can be included with only a little change of the basic technique
described for the scalar case. We discuss applications to the computation of
$n$-body phase space in $D$-dimensional space-time. Substantial simplifications
occur for odd space-time dimensions where the final results can be expressed in
closed form through rational functions. We present explicit analytical formulas
for three-dimensional space-time.
