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Given a convex polygon of $n$ sides, one can draw $n$ disks (called sidedisks) where each disk has a different side of the polygon as diameter and themidpoint of the side as its center. The intersection graph of such disks is theundirected graph with vertices the $n$ disks and two disks are adjacent if andonly if they have a point in common. We prove that for every convex polygonthis graph is planar. Particularly, for $n=5$, this shows that for any convexpentagon 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 theside disks does not contain $K_{3,3}$ as subgraph.

The intersection graph of the disks with diameters the sides of a convex $n$-gon