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 hexagonal prisms with parallel opposite faces are called parallelohedrons and these can tessellate 3-space by translation. In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the Conway criterion will tile the plane. Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration. The Lemoine hexagon is a cyclic hexagon (one inscribed in a