  Let $M$ be a geometrically finite acylindrical hyperbolic 3-manifold and let
$M^*$ denote the interior of the convex core of M. We show that any geodesic
plane in $M^*$ is either closed or dense, and that there are only countably
many closed geodesic planes in $M^*$. These results were obtained earlier by
McMullen, Mohammadi, and the second named author when M is convex cocompact.
  As a corollary we obtain that when $M$ covers an arithmetic hyperbolic
3-manifold $M_0$, the topological behavior of a geodesic plane in $M^*$ is
governed by that of the corresponding plane in $M_0$. We construct a
counterexample of this phenomenon when $M_0$ is non-arithmetic.
