2 problems

Weakly periodic tiling conjecture. There exists a weakly periodic $F$-tiling of $\mathbb Z^d$; more precisely, there exists an $F$-tiling $T\subseteq\mathbb Z^d$ admitting such a f…

Let $V$ be a finite tile in $\mathbb{Z}^n$. A tiling by translations is fully periodic if its translation set has a finite-index period subgroup. Lagarias--Wang conjecture. If $V$…