Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes

Menelaos I. Karavelas, Eleni Tzanaki

Given a set $\Sigma$ of spheres in ${\mathbb{E}}^d$, with $d\ge 3$ and $d$ odd, having a fixed number of $m$ distinct radii ${\rho }_1,{\rho }_2,...,{\rho }_m$, we show that the worst-case combinatorial c…