Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 29 (2022), No. 3, 807--826Copyright Heldermann Verlag 2022 Boundedly Polyhedral Sets and F-Simplices Valeriu Soltan Dept. of Mathematical Sciences, George Mason University, Fairfax, U.S.A. vsoltan@gmu.edu [Abstract-pdf] Generalizing the concept of Choquet simplex, we study a new class of convex solids $K$ in $\mathbb{R}^n$ which satisfy the following condition: all $n$-dimensional intersections of the form $K \cap (x + K)$, $x \in \mathbb{R}^n$, belong to at most finitely many homothety classes of convex solids. Our description of this class uses new results on boundedly polyhedral sets. Keywords: Convex set, Choquet simplex, homothety class, polyhedron. MSC: 52A20. [ Fulltext-pdf  (156  KB)] for subscribers only.