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
Hexagon or circumradius, "R", which equals the side length, "t". The minimal diameter or the diameter of the inscribed circle (separation of parallel sides, flat-to-flat distance, short diagonal or height when resting on a flat base), "d", is twice the minimal radius or inradius, "r". The maxima and minima are related by the same factor: The area of a regular hexagon For any regular polygon, the area can also be expressed in terms of the apothem "a" and the perimeter "p". For the regular hexagon these are given by "a" = "r", and "p"formula_5, so The regular hexagon fills the fraction