On the geometric structure of lattice U-polygons Original Research Article

Let U be a finite set of directions in the Euclidean plane. A convex polygon P is a U-polygon if for each vertex v of P and for each image the line with direction u through v meets a vertex of P different from v. We study the geometric structure of lattice U-polygons and introduce the notion of class of a U-polygon. We then characterize the lattice U-polygons of class image. On the other hand, if P is a lattice U-polygon of class image, we describe a few geometric properties of P.