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The regular dodecahedron has a 2% smaller volume than the rhombicdodecahedron which is the Voronoi cell of a fcc packing. From this point ofview it seems possible that the dodecahedral aspect which is the core of theso-called dodecahedral conjecture, will play a major part for an elementaryproof of the Kepler conjecture. In this paper we will show that the icosahedralconfiguration caused by dodecahedron leads to tetrahedra with significantlylarger volume than the fcc fundamental parallelotope tessellation tetrahedra.Therefore on the basis of a tetrahedral based point of view for sphere packingdensities we will demonstrate the minor importance of the dodecahedron as aVoronoi cell for the Kepler conjecture.

The Dodecahedron as a Voronoi Cell and its (minor) importance for the Kepler conjecture