DANZER-GRüNBAUM'S THEOREM REVISITED

Károly Bezdek; Grigoriy Blekherman

doi:10.1023/a:1004878520642

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 39: Issue 1-3

DANZER-GRüNBAUM'S THEOREM REVISITED

Authors:

Károly Bezdek

Károly Bezdek Eötvös University Department of Geometry H-1053 Budapest Kecskeméti utca 10-12 Hungary E-mail H-1053 Budapest Kecskeméti utca 10-12 Hungary E-mail

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Grigoriy Blekherman

Grigoriy Blekherman Eötvös University Department of Geometry H-1053 Budapest Kecskeméti utca 10-12 Hungary E-mail H-1053 Budapest Kecskeméti utca 10-12 Hungary E-mail

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Pages:: 7–15

Online Publication Date:: 28 Dec 2004

Publication Date:: 01 Dec 2000

Article Category:: Research Article

DOI:: https://doi.org/10.1023/a:1004878520642

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Abstract

In this paper we prove some stronger versions of Danzer-Grnbaum's theorem including the following stability-type result. For 0 < α < 14π/27 the maximum number of vertices of a convex polyhedron in E³ such that all angles between adjacent edges are bounded from above by α is 8. One of the main tools is the spherical geometry version of Pl's theorem.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)