2015/08/12 by Diana Davis, Davis, Diana, Victor Dods +5
Computer Science · Mathematics · #52B10 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Constraint Satisfaction and Optimization #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1508.03546
openalex publication_date 2015/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern--Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics between certain pairs of vertices than other pairs. We also obtain the fact that there are no geodesics that start and end at the same vertex on the regular tetrahedron or the cube.