# On the Existence of $U$-Polygons of Class $cgeq 4$ in Planar Point Sets - Mathematics > Metric Geometry

On the Existence of $U$-Polygons of Class $cgeq 4$ in Planar Point Sets - Mathematics > Metric Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: For a finite set $U$ of directions in the Euclidean plane, a convexnon-degenerate polygon $P$ is called a $U$-polygon if every line parallel to adirection 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 alltheir vertices in certain subsets of the plane and derive explicit results inthe case of cyclotomic model sets.

Author: ** Christian Huck**

Source: https://arxiv.org/