Lines Pinning Lines

Boris Aronov, Otfried Cheong, Xavier Goaoc, Günter Rote

    Research output: Contribution to journalArticlepeer-review


    A line ℓ is a transversal to a family F of convex polytopes in ℝ3 if it intersects every member of F. If, in addition, ℓ is an isolated point of the space of line transversals to F, we say that F is a pinning of ℓ. 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.

    Original languageEnglish (US)
    Pages (from-to)230-260
    Number of pages31
    JournalDiscrete and Computational Geometry
    Issue number2
    StatePublished - Mar 2011


    • Geometric transversal
    • Helly-type theorem
    • Line geometry

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics


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