Friday, November 10, 2017

trihexagonal & rhombille tilings

The image above is the superposition of two tessellations. The dark bold lines show a tiling of the plane that is made up of regular hexagons and triangles (the  trihexagonal tiling).

The light lines show portions of the reciprocal (or dual) of the dark-lined tessellation.

To create a reciprocal tessellation, for every two adjacent tiles in the original tessellation, join the centers of the two tiles by a line segment perpendicular to their shared side. This line segment becomes the edge of one of the tiles in the reciprocal tessellation.

The reciprocal of trihexagonal tiling is made up entirely of rhombs, the rhombille tiling.