##
Introduction to Tessellations (Tilings)

**Regular tessellations**

A regular tessellation is one made up of regular polygons which are all of the same type, and for which all vertexes are of the same type. (A vertex is a point at which three or more tiles meet.) There are only three regular polygons that tessellate in this fashion: equilateral triangles, squares, and regular hexagons.

**Semi-regular tessellations**

A semi-regular tessellation is one made up of two different types of regular polygons, and for which all vertexes are of the same type. There are eight semi-regular tessellations. The three regular and eight semi-regular tessellations are collectively known as the Archimedean tessellations.

**Tessellations around us**

Tessellations are widely used in human design. Examples include floor tilings, brick walls, wallpaper patterns, textile patterns, and stained glass windows. Basically, anytime a surface needs to be covered with units that neither overlap nor leave gaps, tessellations come into play.

**Repeating and non-repeating tessellations**

Tessellations do not have to be repeating, or periodic. In fact, there is a famous family of tessellations based on two tiles known as "Penrose" tiles. These are named after their inventor, English mathematician and theoretical physicist Sir Roger Penrose. When assembled according to a simple set of matching rules, an infinite number of distinct tessellations can be formed by Penrose tiles, and none of them are repeating! These tiles have a number of other interesting properties, many of them related to the Golden Ratio.

Click here to browse products related to tessellations.

Math + Art topics

mathartfun.com home

© 2000-2015 Tessellations