  Given a convex polygon of $n$ sides, one can draw $n$ disks (called side
disks) where each disk has a different side of the polygon as diameter and the
midpoint of the side as its center. The intersection graph of such disks is the
undirected graph with vertices the $n$ disks and two disks are adjacent if and
only if they have a point in common. We prove that for every convex polygon
this graph is planar. Particularly, for $n=5$, this shows that for any convex
pentagon there are two disks among the five side disks that do not intersect,
which means that $K_5$ is never the intersection graph of such five disks. For
$n=6$, we then have that for any convex hexagon the intersection graph of the
side disks does not contain $K_{3,3}$ as subgraph.
