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arXiv · 0811.3546

On the Existence of $U$-Polygons of Class $c\geq 4$ in Planar Point Sets

Christian Huck
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Abstract

For a finite set $U$ of directions in the Euclidean plane, a convex non-degenerate polygon $P$ is called a $U$-polygon if every line parallel to a direction of $U$ that meets a vertex of $P$ also meets another vertex of $P$. We characterize the numbers of edges of $U$-polygons of class $c\geq4$ with all their vertices in certain subsets of the plane and derive explicit results in the case of cyclotomic model sets.

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Christian Huck. 2008-11-21. On the Existence of $U$-Polygons of Class $c\geq 4$ in Planar Point Sets. https://doi.org/10.1016/j.disc.2009.02.035

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