Map coloring problems comprise a classic area of study in topological graph theory, and three-dimensional visualizations of such maps have been a common theme in mathematical art. However, there is a gulf between the mathematical and artistic work because the former is often purely combinatorial. The present work describes how, using known algorithmic techniques, one can visualize these combinatorial maps as so-called “pillowcase models,” a 2D representation first described by Séquin. These models are further adaptable for single-material 3D printing, where the different colors are printed separately and then assembled. The technique is illustrated on examples from the Map Color Theorem, an analogue of the Four Color Theorem for higher-genus surfaces.