  Let $M$ be a convex cocompact acylindrical hyperbolic 3-manifold of infinite
volume, and let $M^*$ denote the interior of the convex core of $M$. In this
paper we show that any geodesic plane in $M^*$ is either closed or dense. We
also show that only countably many planes are closed. These are the first
rigidity theorems for planes in convex cocompact 3-manifolds of infinite volume
that depend only on the topology of M.
