Journal of Geometry

, Volume 52, Issue 1, pp 25–29

On empty convex polytopes


  • Tibor Bisztriczky
    • Department of Mathematics and StatisticsUniversity of Calgary
  • Heiko Harborth
    • Diskrete MathematikTechnische Universität Braunschweig

DOI: 10.1007/BF01406823

Cite this article as:
Bisztriczky, T. & Harborth, H. J Geom (1995) 52: 25. doi:10.1007/BF01406823


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.

Copyright information

© Birkhäuser Verlag 1995