Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 559566 (2006) 

Characterizations of reduced polytopes finitedimensional normed spacesMarek LassakInstitute of Mathematics and Physics, University of Technology, Bydgoszcz 85796, Poland, email: lassak@mail.atr.bydgoszcz.plAbstract: 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.
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