Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 1, pp. 177-193 (2008)

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Approximating $3$-dimensional convex bodies by polytopes with a restricted number of edges

K. J. Böröczky, F. Fodor and V. Vígh

MTA Rényi Institute, 13-15 Reáltanoda u., H-1351 Budapest, Hungary, e-mail: carlos@renyi.hu; Bolyai Institute, University of Szeged, 1 Aradi vértanúk tere, H-6720 Szeged, Hungary, e-mail: fodorf@math.u-szeged-hu e-mail: vigvik@math.u-szeged.hu

Abstract: We prove an asymptotic formula for the Hausdorff distance of a $3$-dimensional convex body $K$ with a $C^2$ boundary and its best approximating circumscribed polytope whose number of edges is restricted.

Keywords: Polytopal approximation, Hausdorff distance, circumscribed polytope

Classification (MSC2000): 52A27, 52A40

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Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.

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