On pyramids and reducedness

Gennadiy Averkov; Horst Martini

doi:10.1007/s10998-008-8117-x

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 57: Issue 2

On pyramids and reducedness

Authors:

Gennadiy Averkov

Gennadiy Averkov University of Magdeburg Faculty of Mathematics D-39106 Magdeburg Germany

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Horst Martini

Horst Martini Chemnitz University of Technology Faculty of Mathematics D-09107 Chemnitz Germany

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Pages:: 117–120

Online Publication Date:: 10 Dec 2008

Publication Date:: 01 Dec 2008

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10998-008-8117-x

Keywords:: 52A20; 52B12; 52A40; geometric inequality; pyramid; minimum width; reduced body; thickness

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Abstract

A convex body K in ℝ^d is said to be reduced if the minimum width of each convex body properly contained in K is strictly smaller than the minimum width of K. We study the question of Lassak on the existence of reduced polytopes of dimension larger than two. We show that a pyramid of dimension larger than two with equal numbers of facets and vertices is not reduced. This generalizes the main result from [8].

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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)