Abstract
A long-standing collaboration between an artist and a mathematician bears new fruit in the form of novel geometric constructions and several works of art based on them. The inspiration for the present collaboration is a recent result on the edge-length ratios between dual regular dodecahedra and icosahedra, specifically the two vertex-to-face pairings of these dual Platonic solids: when the icosahedron circumscribes the dodecahedron, the edge-length ratio is 𝜙/3, and conversely, when the dodecahedron circumscribes the icosahedron, the edge-length ratio is 𝜙2/√5, where 𝜙 is the golden number. These two edge-length ratios are the basis for the geometric constructions and the resulting artwork, which highlight interesting characteristics of the two ratios, both individually and as they relate to each other.
