Discrete & Computational Geometry

, Volume 45, Issue 2, pp 230–260 | Cite as

Lines Pinning Lines

  • Boris Aronov
  • Otfried Cheong
  • Xavier Goaoc
  • Günter Rote


A line is a transversal to a family F of convex polytopes in ℝ3 if it intersects every member of F. If, in addition, is an isolated point of the space of line transversals to F, we say that F is a pinning of . We show that any minimal pinning of a line by polytopes in ℝ3 such that no face of a polytope is coplanar with the line has size at most eight. If in addition the polytopes are pairwise disjoint, then it has size at most six.


Geometric transversal Helly-type theorem Line geometry 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Boris Aronov
    • 1
  • Otfried Cheong
    • 2
  • Xavier Goaoc
    • 3
  • Günter Rote
    • 4
  1. 1.Department of Computer Science and EngineeringPolytechnic Institute of NYUNew YorkUSA
  2. 2.Department of Computer ScienceKAISTDaejeonKorea
  3. 3.LORIA - INRIA Nancy Grand EstNancyFrance
  4. 4.Institut für InformatikFreie Universität BerlinBerlinGermany

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