2013/12/12 by Kaysilyn Lawson, James L. Parish, Cynthia M. Traub +1 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Simple (philosophy) #Regular polygon #Geodesic #Mathematics #Combinatorics #Computer science #Geometry #Philosophy #Epistemology
paper · pdf · doi:10.12732/ijpam.v89i2.1
openalex publication_date 2013/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
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.