On some characterizations of convex polyhedra

TL;DR

This paper establishes new necessary and sufficient conditions based on sections and projections that characterize convex bodies as polytopes, enhancing understanding of their geometric properties.

Contribution

It introduces two novel criteria involving sections and projections that precisely characterize convex polyhedra.

Findings

Conditions are both necessary and sufficient

Criteria involve geometric sections and projections

Advances characterization of convex polyhedra

Abstract

This work provides two sufficient conditions in terms of sections or projections for a convex body to be a polytope. These conditions are necessary as well.