The Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell Conjecture

Deep Bhattacharjee, Ushashi Bhattacharya, Priyabrata Mandal +1

We prove that every Voronoi cell of a unit-ball packing of ${\mathbb{R}}^4$ has volume at least $8$, with equality only at the $D_4$ configuration, so that the twenty-four-cell conje…