An illumination problem for zonoids
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Let Z ⊂ E d be ad-dimensional zonoid, whered≥3. Boltjanskii and Soltan recently proved that if Z is not a parallelotope, then Z can be illuminated by 3·2d−2 points disjoint from Z. In the present paper we prove a related result. Namely, we show that ifd+1=2 p , then Z can be illuminated by 2 d /d+1 lines lying outside Z.
KeywordsBoundary Point Convex Body Convex Polytope Edge Graph Affine Subspace
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- K. Bezdek,Hadwiger-Levi’s covering problem revisited, inNew Trends in Discrete and Computational Geometry (J. Pach, ed.), Springer-Verlag, Berlin, pp. 199–233 (to appear).Google Scholar
- V. G. Boltjanskii and P. S. Soltan,Solution of Hadwiger’s problem for a class of convex bodies, Soviet Math. Dokl.42 (1990), 18–22.Google Scholar
- R. Schneider and W. Weil,Zonoids and related topics, inConvexity and its Applications (P. M. Gruber and J. M. Wills, eds.), Birkhäuser, 1983, pp. 296–317.Google Scholar