Abstract
Letn andd be integers,n>d ≥ 2. We examine the smallest integerg(n,d) such that any setS of at leastg(n,d) points, in general position in Ed, containsn points which are the vertices of an empty convexd-polytopeP, that is, S∩intP = 0. In particular we show thatg(d+k, d) = d+2k−1 for 1 ≤k ≤ iLd/2rL+1.
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Bisztriczky, T., Harborth, H. On empty convex polytopes. J Geom 52, 25–29 (1995). https://doi.org/10.1007/BF01406823
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DOI: https://doi.org/10.1007/BF01406823