6 problems

Let $I=[0,1)^d$, and let $T\subseteq \mathbb{R}^d$ be such that $I+T$ is a 2-extremal cube-tiling of $\mathbb{R}^d$, meaning a tiling satisfying the 2-extremality condition used in…

Let ${\cal CP}$ be a non-extendible $d$-dimensional cube packing with $2^d-\delta$ cubes. Its lifting is the $(d+1)$-dimensional non-extendible cube packing obtained by adding a la…

Let $P$ be a non-extensible cube packing with $2^n-l$ cubes, and let $H(P)$ be its complement, called a hole. The source considers holes for cube packings in any dimension. Finite-…

Let $P$ be a non-extensible cube packing with $2^n-l$ cubes, and let $H(P)$ be its complement, called a hole. The source considers holes for cube packings of class ${\mathcal P}_2$…

Even-dimensional parameter-count conjecture. There exist non-extensible combinatorial torus cube packings with $n+2$ cubes and

Parameter bound conjecture. The number of parameters is at most