Tessellation - Regular and Semi-regular Tessellations

Regular and Semi-regular Tessellations

A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. A semi-regular tessellation uses a variety of regular polygons, of which there are eight. The arrangement of polygons at every vertex point is identical. An edge-to-edge tessellation is even less regular: the only requirement is that adjacent tiles only share full sides, i.e., no tile shares a partial side with any other tile. Other types of tessellations exist, depending on types of figures and types of pattern. There are regular versus irregular, periodic versus nonperiodic, symmetric versus asymmetric, and fractal tessellations, as well as other classifications.

Penrose tilings using two different polygons are the most famous example of tessellations that create aperiodic patterns. They belong to a general class of aperiodic tilings that can be constructed out of self-replicating sets of polygons by using recursion.

A monohedral tiling is a tessellation in which all tiles are congruent. Spiral monohedral tilings include the Voderberg tiling discovered by Hans Voderberg in 1936, whose unit tile is a nonconvex enneagon; and the Hirschhorn tiling discovered by Michael Hirschhorn in the 1970s, whose unit tile is an irregular pentagon.