Vertex-to-Self Trajectories on the Platonic Solids

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Vertex-to-Self Trajectories on the Platonic Solids

We 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.

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Mathematical subjects

Geometry and Topology

Connections to other fields

Physics

Author(s)

Jayadev S. Athreya, David Aulicino

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DOI (Digital Object Identifier)

10.14760/SNAP-2020-003-EN

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snapshots-2020-003.pdf

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