This paper documents the permutational development of artist James Mai’s painting Shiva: World Ages and discusses two ways Burnside’s Lemma can be seen to be at work in this painting, including which way is more appropriate. Ultimately, the authors examine the impact of the investigation on the artist’s prior assumptions about the arc-forms as a set, and how new realizations about their relationships contribute to both the compositional organization and the metaphoric references indicated by the painting’s title.