Boundedly Polyhedral Sets and F-Simplices

Generalizing the concept of Choquet simplex, we study a new class of convex solids

in

\mathbb{R}^n R n

which satisfy the following condition: all

n n

-dimensional intersections of the form

K \cap (x + K) K ∩ ( x + K )

,

x \in \mathbb{R}^n x ∈ 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.