HH-triangles with kk interior HH-points

An HH-triangle is a triangle with corners in the set of vertices of a tiling of R2R2 by regular hexagons of unit edge. It is known that any HH-triangle with exactly 1 interior HH-point can have at most 10 HH-points on its boundary. In this note we prove that any HH-triangle with exactly kk interior HH-points can have at most 3k+73k+7 boundary HH-points. Moreover we form two conjectures dealing with HH-polygons.