2019/04/12 by Max Leppmeier, Leppmeier, Max
Mathematics · Physics and Astronomy · #00 #51 #52 #Advanced Mathematical Theories and Applications #FOS: Mathematics #History and Developments in Astronomy #History and Overview (math.HO) #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1904.06108
openalex publication_date 2019/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The regular dodecahedron has a 2% smaller volume than the rhombic dodecahedron which is the Voronoi cell of a fcc packing. From this point of view it seems possible that the dodecahedral aspect which is the core of the so-called dodecahedral conjecture, will play a major part for an elementary proof of the Kepler conjecture. In this paper we will show that the icosahedral configuration caused by dodecahedron leads to tetrahedra with significantly larger volume than the fcc fundamental parallelotope tessellation tetrahedra. Therefore on the basis of a tetrahedral based point of view for sphere packing densities we will demonstrate the minor importance of the dodecahedron as a Voronoi cell for the Kepler conjecture.