This paper will illustrate the mathematical underpinnings of some of the most well-known and best-preserved artistic designs of Islamic Spain from the 13th - 15th centuries. The art objects incorporating these elaborate designs include geometric mosaics, decorative ceramic work, carvings in ivory and wood, and metal work. Slides of the objects will be shown and their idealized geometrical structure then. explored with the aid of computer-drawn compass and straightedge constructions, using the Geometer's Sketchpad software. The crystallographic symmetry group, and the affect of colorings on this, may also be discussed for each design.