A Trajectory from a Vertex to Itself on the Dodecahedron

TL;DR

This paper proves the existence of a special geodesic trajectory on the dodecahedron that starts and ends at the same vertex without passing through any other vertices, revealing new geometric properties.

Contribution

It establishes the existence of a vertex-to-self geodesic on the dodecahedron that avoids all other vertices, a novel geometric result.

Findings

Existence of a vertex-to-self geodesic on the dodecahedron

Trajectory does not pass through any other vertices

New insights into dodecahedron geometry

Abstract

We prove that there exists a geodesic trajectory on the dodecahedron from a vertex to itself that does not pass through any other vertex.