Yellow Brick Road Path on Regular Dodecahedron

thingiverse

This is a regular dodecahedron, split into two parts along the "Yellow Brick Road," the unique simple closed path that solves the antisocial jogger problem for any of the Platonic solids. Such a path must (1) begin and end at a single vertex of the solid, and (2) be a straight line path that may cross over edges, but may not pass through any other vertices. The trajectory is described in a paper from 2109 by mathematicians Jayadev Athreya and David Aulicino, and summarized beautifully in a Numberphile video: A New Discovery about Dodecahedrons - Numberphile: https://www.youtube.com/watch?v=G9_l8QASobI A Trajectory from a Vertex to Itself on the Dodecahedron: https://arxiv.org/abs/1802.00811 Two versions of the 3D printable model are provided. One has no connectors to secure the two parts together, the other has tabs and recesses and will hold together with friction. No rafts or supports are needed to print either part. The print in the photo was scaled down to 60%.