On the interior H-points of H-polygons

An H-polygon is a simple polygon whose vertices are H-points, which are points of the set of vertices of a tiling of R-2 by regular hexagons of unit edge. Let G(v) denote the least possible number of H-points in the interior of a convex H-polygon K with v vertices. In this paper we prove that G(8) = 2, G(9) = 4, G(10) = 6 and G(v) >= left perpendicular v(3)/16 pi(2) - v/4 + 1/2 right perpendicular - 1 for all v >= 11, where [x] denotes the minimal integer more than or equal to x.