In the spirit of Pisanski (1989) we consider orientable quadrilateral embeddings of Cartesian products of cycles on surfaces. We offer a constructive example of such an embedding of three low-order cycles. Then we show more generally that such embeddings exist for products of the form $C_2\times C_{2n}\times C_m$. We represent our graphs using rotation schemes to show this existence. Use of rotation schemes led to the ultimate characterization of our findings visually, providing conjectures for generalizations of products of three cycles.

Authors: Matthew Farnsworth, Maxwell Goskie, Jackson Sayre, Adrian Volpe; Advisor: Dr. Blake Dunshee