One of the most prominent forms of information transmission between nano- or micro-scale devices is molecular communication, where molecules are used to transfer information inside a fluidic channel. The effects of channel shape on achievable information transmission rates is considered in this work. Specifically, regular convex polygons are studied. A mathematical framework for finding the optimal channel among this class of geometric shapes is derived. Using this framework it is shown that the optimal channel tends to be circular. This result is verified using computer simulations.