Cellular resolutions have been an area of active interest in the study of monomial ideals in the past few years. A cellular resolution is a way of encoding the information of the free resolution of an ideal in a cell complex. We will study the Stanley-Reisner rings arising from the simplicial polytopes known as the cyclic polytopes. These polytopes have the interesting property that they maximize all entries in the f-vector of the set of polytopes with fixed dimension and vertices. I will explain a little of the background theory and then cover the main idea of the construction.