Areas of generalized \(H\)-polygons (Q1352876)

The authors consider tilings of the euclidean plane by regular hexagons, and denote the set of its vertices by \(V\). The union of a finite number of such hexagons with the property that its boundary is a simple closed polygonal curve, is called a simple \(V\)-polygon. Then the authors give a Pick-type theorem in terms of the area, the number of \(V\)-points and a less obvious functional.