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The Surface Area Deviation of the Euclidean Ball and a Polytope

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Abstract

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices or facets in the symmetric surface area deviation.

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Correspondence to Elisabeth M. Werner.

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Elisabeth M. Werner was partially supported by an NSF grant.

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Hoehner, S.D., Schütt, C. & Werner, E.M. The Surface Area Deviation of the Euclidean Ball and a Polytope. J Theor Probab 31, 244–267 (2018). https://doi.org/10.1007/s10959-016-0701-9

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  • DOI: https://doi.org/10.1007/s10959-016-0701-9

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Mathematics Subject Classification (2010)