# Tessellation

A **Tessellation** is a regular tiling of the infinite plane by polygons, or of an infinite three dimensional space by polyhedra, or of an infinite n-dimensional space by polytopes.

### Plane Tessellations

Tessellations of the plane can be classified as follows:

**Regular Tesselations** are comprised of simple repetitions of the same regular polygon. There are three distinct regular tessellations: equilateral triangles, squares and hexagons.

**Semiregular Tessellations** are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is the same for all vertices in the plane. There are *eight* such semiregular tessellations. These are often referred to as Archimedean tessellations.

**Demiregular Tessellations** are comprised of repetitions of two or more regular polygons, where the number and type of each kind of polygon surrounding each vertex is different for some of the vertices in the plane. Although it can be argued that the number of such tessellations is infinite, they can be reduced to 14 specific types.

Other tessellations of the plane exist. See for example the tilings of M.C. Escher.