Rhombille tiling

In geometry, the rhombille tiling,[1] also known as tumbling blocks,[2] reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane.

Thus, the rhombille tiling can be viewed as an example of an infinite unit distance graph and partial cube.

[16] In quilting, it has been known since the 1850s as the "tumbling blocks" pattern, referring to the visual dissonance caused by its doubled three-dimensional interpretation.

[2][15][17] As a quilting pattern it also has many other names including cubework, heavenly stairs, and Pandora's box.

[17] It has been suggested that the tumbling blocks quilt pattern was used as a signal in the Underground Railroad: when slaves saw it hung on a fence, they were to box up their belongings and escape.

There is a single known instance of implicit rhombille and trihexagonal tiling in English heraldry – in the Geal/e arms.

It is one of several repeating structures used to investigate Ising models and related systems of spin interactions in diatomic crystals,[21] and it has also been studied in percolation theory.

Rhombus unit for the rhombille tiling dual to unit-length trihexagonal tiling.
Two hexagonal tilings with red and blue edges within rhombille tiling
Four hexagonal tilings with red, green, blue, and magenta edges within the rhombille tiling [ 3 ]