Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 559-566 (2006)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Characterizations of reduced polytopes finite-dimensional normed spaces

Marek Lassak

Institute of Mathematics and Physics, University of Technology, Bydgoszcz 85-796, Poland, e-mail:

Abstract: A convex body $R$ in a normed $d$-dimensional space $M^d$ is called reduced if the $M^d$-thickness $\Delta (K)$ of each convex body $K\subset R$ different from $R$ is smaller than $\Delta (R)$. We present two characterizations of reduced polytopes in $M^d$. One of them is that a convex polytope $P \subset M^d$ is reduced if and only if through every vertex $v$ of $P$ a hyperplane strictly supporting $P$ passes such that the $M^d$-width of $P$ in the perpendicular direction is $\Delta (P)$. Also two characterization of reduced simplices in $M^d$ and a characterization of reduced polygons in $M^2$ are given.

Keywords: reduced body, reduced polytope, normed space, width, thickness, chord

Classification (MSC2000): 52A21, 52B11, 46B20

Full text of the article:

Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.

© 2007 Heldermann Verlag
© 2007–2009 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition