  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.
