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- Publisher
- de Gruyter
- Copyright
- Copyright © 2001 by Walter de Gruyter GmbH & Co. KG
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/form.2001.012
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. There exist positive constants c0 and c1 c1 n such that for every 0 ` e ` 1a2 the n following holds: Let P be a convex polytope in Rn having N c0 ae vertices x1 Y F F F Y xN . Then there exists a subset A r f1Y F F F Y Ng, cardA 1 À 2eN, such that for all i e A voln P À voln convvertPnfxi g c1 neÀn1anÀ1 N Àn1anÀ1 X voln P n Also, if P is a convex polytope in Rn having N c0 ae facets. Let Hi be the half space determined by the facet Fi , which contains P i 1Y F F F Y N. Then there exists a subset A r f1Y F F F Y Ng, cardA 1 À 2eN, such that for all i e A voln jHi Hj À voln P voln P c1 neÀn1anÀ1 N Àn1anÀ1 X 1991 Mathematics Subject Classi®cation: 52A22. 1 Introduction In the last three decades, a number of papers have been published that deal with approximation of convex bodies in the Euclidean space Rn by convex polytopes. The precision of the approximation is being measured using
Journal
Forum Mathematicum – de Gruyter
Published: Apr 5, 2001