Let the ***simplex cover*** of a finite set $\mathcal{P}\subset \mathbb{E}^n,\ n\,\le\, k:=\operatorname{card}(\mathcal{P})\,\lt\infty$ of points in Euclidean $n$-space, denote a maximal interior-disjoint set of $n$-simplices with every corner an element of $\mathcal{P}$. <br> >**Questions:** >letting $\mathrm{H}_\Sigma$ denote the set of simplex-sides, that are ***not*** shared by two simplices, >- is $\mathrm{H}_\Sigma$ an invariant after a change of the *simplex covers* of a fixed pointset $\mathcal{P}$? - is $\mathrm{H}_\Sigma$ identical to the set of facets of the convex hull $\mathrm{CH}(\mathcal{P})$? The reason for asking is the idea to base the definition of geometric hulls of discrete pointsets on the simplex-faces that are not shared by simplices by certain "regular" simplex-coverings of a pointset, provided the set of those undhared sides is invariant among all admissible coverings.