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- ItemVertex-to-Self Trajectories on the Platonic Solids(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Athreya, Jayadev S.; Aulicino, DavidWe consider the problem of walking in a straight line on the surface of a Platonic solid. While the tetrahedron, octahedron, cube, and icosahedron all exhibit the same behavior, we find a remarkable difference with the dodecahedron.