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Approximation of the sphere by polytopes having few vertices

Authors: I. Bárány and Z. Füredi
Journal: Proc. Amer. Math. Soc. 102 (1988), 651-659
MSC: Primary 52A40; Secondary 52A22
MathSciNet review: 928998
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Abstract: How well can a polytope with $ n$ vertices approximate the unit ball $ {B^d}$ of the $ d$-dimensional Euclidean space? The answer is quite well known when $ d$ is fixed and $ n$ tends to infinity. In this paper the same question is answered when $ n$ is a function of $ d$ (a polynomial in $ d$, say) and $ d$ tends to infinity. Some applications of the results are also indicated.

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