VERTEX TO VERTEX GEODESICS ON PLATONIC SOLIDS

Serge Troubetzkoy (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Systèmes dynamiques [math.DS]

Serge Troubetzkoy. VERTEX TO VERTEX GEODESICS ON PLATONIC SOLIDS. The American Mathematical Monthly, 2022, pp.379-382. ⟨10.1080/00029890.2023.2172298⟩. ⟨hal-03563408v3⟩