The sparse zonotope approximation conjecture

Let $K\subseteq\mathbb{R}^d$ be a zonotope and let $0<\varepsilon\leq\frac12$. A zonotope is a Minkowski sum of finitely many line segments; its number of segments is the number of summands. Sparse zonotope approximation conjecture. There exists a zonotope $Q$ with $O(d/\varepsilon^2)$ segments such that

$$Q\subseteq K\subseteq(1+\varepsilon)Q.$$

This is the main open question about approximating a $d$-dimensional zonotope by one with only linearly many segments, and it is attributed in the source to the AIM workshop.