Document Zbl 1277.05029

A short proof of Klee’s theorem. (English) Zbl 1277.05029

Discrete Math. 314, 14-16 (2014).

Summary: In 1959, V. Klee [Acta Math. 102, 79–107 (1959; Zbl 0094.16802)] 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 \(\mathbb{R}^3\).

Cited in 1 Document

MSC:

05B25	Combinatorial aspects of finite geometries
52A99	General convexity

Keywords:

convex body; polyhedra; polar dual; Victor Klee; projection; polygon

Citations:

Zbl 0094.16802

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Full Text: DOI arXiv

References:

[1]	Klee, V., Some characterizations of convex polyhedra, Acta Math., 102, 79-107 (1959) · Zbl 0094.16802
[2]	Mirkil, H., New characterizations of polyhedral cones, Canad. J. Math., 9, 1-4 (1957) · Zbl 0083.38302

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