Artist James Mai created a system of forms in the developmental stages of his work Epicycles. This system offered mathematician Daylene Zielinski opportunities to provide mathematical analysis and to contribute to the final compositional organization of Epicycles. A set of eight new permutational forms are developed from a revised interrogation of a previously developed system of eighteen forms. The new set of forms lends itself to a variety of compositional arrangements including, with contributions from Zielinski, a “braided” ordering that creates a coherent sequence of the forms in the final work. This paper not only explicates the system of forms used in the resulting work, but it also illustrates the benefits and insights gained from interdisciplinary interactions between an artist and a mathematician during the development of a mathematically based work of art.