3 problems

Let $O$, $C$ and $T$ denote the regular octahedron, cuboctahedron and regular tetrahedron, respectively. For a convex body $K$, let $\delta^t(K)$ denote its maximal translative pac…

Let $K$ be a solid, such as a tetrahedron, cuboctahedron or octahedron. Its maximal translative packing density is the supremum of densities of packings by translates of $K$, and i…

Let $K$ be a three-dimensional centrally symmetric convex body. For a set $V$ of unit vectors, define … with the minimization over the points ${\bf x}_j\in X$ as in the source. Con…