The cosimple zonotope covering-radius conjecture

Let a finite collection of lattice vectors spanning $\mathbb{R}^d$ be cosimple if it has a linear dependence whose coefficients are all non-zero and have pairwise different absolute values. A lattice zonotope generated by a cosimple collection is a cosimple zonotope. Cosimple zonotope covering-radius conjecture. Every cosimple zonotope with generators in $\mathbb{Z}^d$ has covering radius at most

$$\frac{d}{d+2}.$$

This conjecture generalizes the shifted Lonely Runner Conjecture because every Strong Lonely Runner Zonotope with $n$ generators is a cosimple $(n-1)$-zonotope. The paper introduces it to address the fact that projections of Strong Lonely Runner Zonotopes need not remain Strong Lonely Runner Zonotopes; its general status is open.