3 problems

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…

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…