Geodesic trajectories on regular polyhedra
Metric Geometry
2015-08-17 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.1508.03546,
title = {Geodesic trajectories on regular polyhedra},
author = {Diana Davis and Victor Dods and Cynthia Traub and Jed Yang},
journal= {arXiv preprint arXiv:1508.03546},
year = {2015}
}
Comments
15 pages, 9 figures