Flapping Polyhedra: an Unfolding Story

Rick Mabry, LSU Shreveport

It has been known for a few decades that there exist 43380 distinct nets (edge unfoldings) of the icosahedron, and that this is (therefore) likewise true for the dodecahedron. The complete set of such nets has only recently  been constructed, by three teams working independently. We look at the various  ways this was achieved, consider some consequences and applications, view  some "flappers" (animations), and maybe get a bit silly.