  Tverberg's theorem says that a set with sufficiently many points in
$\mathbb{R}^d$ can always be partitioned into $m$ parts so that the
$(m-1)$-simplex is the (nerve) intersection pattern of the convex hulls of the
parts. The main results of our paper demonstrate that Tverberg's theorem is but
a special case of a more general situation. Given sufficiently many points, all
trees and cycles can also be induced by at least one partition of a point set.
