The Minimum Number of Interior $H$-Points of Convex $H$- Dodecagons

An $H$-polygon is a simple polygon whose vertices are $H$-points, which are points of the set of vertices of a tiling of $\mathbb{R}^{2}$ 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 $G(12)=12$.