2 problems

Let $d=3$ and $n=2k$, and let $\widehat{\Sigma}_k$ denote the $k$th higher secondary polytope of the configuration. Farber's conjecture. The diameter of $\widehat{\Sigma}_k$ is … T…

Let $\mathcal{A}\subset\mathbb{R}^{d-1}$ be a configuration of distinct points, and let $\widehat{\Sigma}_{\mathcal{A},k}$ be the convex hull of the vectors…