… with charged polygons

Indecomposable coverings with homothetic polygons

We prove that for any polygon S with at least four sides, and any k > 0, there is a k-fold covering of the plane with homothetic copies of S that can not be decomposed into two coverings.

Mapping rates associated with polygons

Suppose that geographic data under investigation are rates associated with polygons. For example, disease incidence, mortality, and census undercount data may be displayed as rates. Spatial analysis of data of this sort can be handled very naturally through Bayesian hierarchical statistical modeling, where there is a measurement process at the ®rst level, an explanatory process at the second le...

Tiling with Regular Star Polygons

The Archimedean tilings (Figure 1) and polyhedra will be familiar to many readers. They have the property that the tiles of the tiling, or the faces of the polyhedron, are regular polygons, and that the vertices form a single orbit under the symmetries of the tiling or polyhedron. (Grünbaum and Shephard [1] use Archimedean, in relation to tilings, to refer to the sequence of polygons at each ve...

Convexifying polygons with simple projections

Tiling Polygons with Lattice Triangles

Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are ratio...