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Lines Pinning Lines.

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Title: Lines Pinning Lines.
Authors: Aronov, Boris1 aronov@poly.edu, Cheong, Otfried2 otfried@kaist.edu, Goaoc, Xavier3 goaoc@loria.fr, Rote, Günter4 rote@inf.fu-berlin.de
Source: Discrete & Computational Geometry. Mar2011, Vol. 45 Issue 2, p230-260. 31p.
Subjects: Convex polytopes, Line geometry, Polytopes, Orthogonal polynomials, Convex geometry
Abstract: line ℓ is a transversal to a family F of convex polytopes in ℝ 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 ℝ 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. [ABSTRACT FROM AUTHOR]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="DE" term="%22Convex+polytopes%22">Convex polytopes</searchLink><br /><searchLink fieldCode="DE" term="%22Line+geometry%22">Line geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Polytopes%22">Polytopes</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+geometry%22">Convex geometry</searchLink>
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  Data: line ℓ is a transversal to a family F of convex polytopes in ℝ 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 ℝ 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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