3 problems

Let $P$ be any packing of unit spheres in $\mathbb{R}^4$, and consider its Voronoi decomposition. Let the volume of a regular 24-cell circumscribed about a unit sphere be the refer…

Consider a packing of unit balls in three-dimensional Euclidean space, and let a Voronoi cell be the region of points at least as close to its ball's center as to the centers of al…

Let $O$ and $C$ denote the regular octahedron and cuboctahedron, respectively. For a centrally symmetric convex body $K$, let $\delta(K)$ be the density obtained from the minimum v…