Vertex to vertex geodesics on platonic solids

2022/02/10 by Serge Troubetzkoy, Troubetzkoy, Serge
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #History and Theory of Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2202.04892

openalex publication_date 2022/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a simple proof based on symmetries that there are no geodesics from a vertex to itself in the cube, tetrahedron, octahedron, and icosahedron.

Related

• Geodesic trajectories on regular polyhedra
• Simple closed geodesics on regular spherical polyhedra
• A Trajectory from a Vertex to Itself on the Dodecahedron
• Closed simple geodesics on a polyhedron
• Simple Closed Quasigeodesics on Tetrahedra