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.

Properties

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 tiling. It can also be seen as a subdivision of four hexagonal tilings with each hexagon divided into 12 rhombi.

The diagonals of each rhomb are in the ratio 1:√3. This is the dual tiling of the trihexagonal tiling or kagome lattice. As the dual to a uniform tiling, it is one of eleven possible Laves tilings, and in the face configuration for monohedral tilings it is denoted [3.6.3.6].

It is also one of 56 possible isohedral tilings by quadrilaterals, and one of only eight tilings of the plane in which every edge lies on a line of symmetry of the tiling.