Rhombille tiling

The rhombille tiling is an isohedral tiling with rhombi for faces, joining 3 or 6 to a vertex. It is the dual of the uniform trihexagonal tiling.

Each face of this tiling is a rhombus with longer diagonal $$\sqrt3 ≈ 1.73205$$ times the shorter diagonal, with an acute angle of 60° and an obtuse angle of 120°. These rhombi can be split along their short diagonal into two equilateral triangles; if all the rhombi area split this way, the result is the regular triangular tiling.