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arXiv · 1002.3294

Lines pinning lines

Boris Aronov·Otfried Cheong·Xavier Goaoc·Günter Rote
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Abstract

A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show that any minimal pinning of a line by convex polytopes such that no face of a polytope is coplanar with the line has size at most eight. If, in addition, the polytopes are disjoint, then it has size at most six. We completely characterize configurations of disjoint polytopes that form minimal pinnings of a line.

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Boris Aronov, Otfried Cheong, Xavier Goaoc, Günter Rote. 2010-02-17. Lines pinning lines. https://doi.org/10.1007/s00454-010-9288-6

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