H-triangles with 3 interior H-points

Abstract

H -triangle is a triangle with corners in the set of vertices of a tiling of R 2 by regular hexagons of unit edge. Let b( ) be the number of the boundary H -points of an H -triangle . In this note we prove that any H -triangle with exactly 3 interior H -points can have 3,4,5,6, 7, 8, 9, 10, 11, 12, 13, 14 or 16 H -points on its boundary.