Given a regular hexagon and a triangle both having a common edge, there exists a ring of five extra triangles each sharing an edge with the hexagon, as well as a ring of regular hexagons surrounding the triangles and having two edges in common with two successive triangles. Surrounding each new hexagon in the same manner by triangles and hexagons, a tiling of triangles and hexagons is produced. The authors prove that all the triangles of such a tiling have the same left isodynamic point. Moreover they show that each such tiling can be obtained via a transformation in the complex plane of a semiregular tiling of the plane by regular hexagons and regular triangles.