A Short Proof of Klee's Theorem

TL;DR

This paper presents a new proof of Klee's theorem, which characterizes convex polyhedra in three-dimensional space based on their projections being polygons, offering a potentially simpler or different approach from previous proofs.

Contribution

The paper provides a novel proof of Klee's theorem specifically for convex bodies in three dimensions, expanding understanding of convex geometry.

Findings

New proof of Klee's theorem for 3D convex bodies

Convex bodies are polyhedra iff all projections are polygons

Simplifies understanding of convex polyhedra characterization

Abstract

In 1959, Klee proved that a convex body $K$ is a polyhedron if and only if all of its projections are polygons. In this paper, a new proof of this theorem is given for convex bodies in $\mathbb{R}^3$.