COLORING GRAPHS TO CLASSIFY SIMPLE CLOSED GEODESICS ON CONVEX DELTAHEDRA
Kaysilyn Lawson, James L. Parish, Cynthia M. Traub, Adam G. Weyhaupt · International Journal of Pure and Apllied Mathematics · 2013
We obtain a complete classification of all simple closed geodesics on the eight convex deltahedra by solving a related graph coloring problem.Geodesic segments in the neighborhood of each deltahedron vertex produce a limited number of crossing angles with deltahedron edges.We define a coloring on the edge graph of a deltahedron based on these angles, and we show that the set of graph colorings compatible with edge-colorings of the neighborhood graphs of radius one classifies all possible simple closed geodesics on all convex deltahedra.