Boris Aronov, Otfried Cheong, Xavier Goaoc, and Günter Rote:
Lines pinning lines
Discrete and Computational Geometry
45 (2011), 230–260. doi:10.1007/s00454-010-9288-6,
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.
Last update: August 15, 2017.