The zonotopal reformulation of the Lonely Runner Conjecture

Let $n$ be a positive integer. Let $Z\subseteq\mathbb{R}^n$ be a zonotope generated by $n+1$ vectors of $\mathbb{Z}^n$ in LGP (general linear position), and let $\boldsymbol{x}$ be the center of $Z$. The zonotopal reformulation of the Lonely Runner Conjecture. Then

$$\left(\boldsymbol{x}+\frac{n}{n+2}(Z-\boldsymbol{x})\right)\cap\mathbb{Z}^n\neq\varnothing.$$

This reformulates the Lonely Runner Conjecture as a lattice-point assertion for a homothetic copy of a centered lattice zonotope. Its resolution is therefore tied to the unresolved cases of the Lonely Runner Conjecture; the source gives no separate resolution evidence.