3 problems

Let $K$ be a convex body, and let $H(K)$ denote its Hadwiger number, the maximum number of translates of $K$ that can touch one given translate without overlapping interiors. Grünb…

Let $T$ be a tetrahedron, and let $H(T)$ denote its Hadwiger number, the maximum number of translates of $T$ that can touch one given translate without overlapping interiors. Zong'…

Let $F,B\subset\mathbb{R}^d$ be convex domains, and let $N(F,B)$ denote the set of generalized Hadwiger numbers associated with $F$ and $B$. For consecutive elements of $N(F,B)$, c…