Rhombille tiling Rhombille tiling In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles and sets of six rhombi meet at their 60° angles. The rhombille tiling can be seen as a subdivision of a hexagonal tiling with each hexagon divided into three rhombi meeting at the center point of the hexagon. This subdivision represents a regular compound
Heesch's problem a tile may be surrounded, its Heesch number is said to be infinite. In this case, an argument based on Kőnig's lemma can be used to show that there exists a tessellation of the whole plane by congruent copies of the tile. Consider the non-convex polygon "P" shown in the figure to the right, which is formed from a regular hexagon by adding projections on two of its sides and matching indentations on three sides. The figure shows a tessellation consisting of 61 copies of "P", one large infinite region, and four small diamond-shaped polygons within the fourth layer. The