A Skeleton Key for the Platonic Solids

Karl Schaffer
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 199–206 Regular Papers


Dance performances in which dancers wield sections of PVC pipe to form a number of polyhedral designs led to the question: what is the largest graph which edge decomposes the “skeletons” of all five Platonic solids? We show that a certain 6-edge tree is the largest such graph, and investigate related questions.