# What is a tessellation?

fun stuff > what is a tessellation?

*Page updated : 11 April 2018 *

A tessellation is a regular pattern made up of flat shapes repeated
and joined together without any gaps or overlaps. These shapes do not
all need to be the same, but the pattern should repeat. Another word
for tessellation is **tiling**.

**Here are some tessellation examples...**

The word tessellation is derived from the Greek "tesseres", which means "four" and refers to the four sides of a square, the first shape to be tiled.

## Regular Tessellations

A **regular tessellation** is a pattern made by repeating
a regular polygon. A **regular polygon** is one having all its sides equal
and all it's interior angles equal.

So there are only 3 kinds of regular tessellations - ones made from squares, equilateral triangles and hexagons.

Where the shapes join together, the corner point, we call that** the
vertex**. By looking at the vertex and counting the sides of all
the shapes that meet at the vertex you are able to name a tessellation.

**For example...**

Choose a vertex
and count the sides of the polygons that touch it. In the example above
of a regular tessellation of hexagons, next to the vertex are three
polygons and each has six sides, so this tessellation is called "**6.6.6**".

## Semi-Regular Tessellations

A **semi-regular tessellation** is made of two or more
regular polygons e.g the hexagon and diamond shape above. The pattern
at each vertex should be the same.

There are only 8 semi-regular tessellations...

## Other Tessellations

There are also **demi-regular tessellations** or **polymorph
tessellations**,
but they are difficult to define. Some have described them as a tilings
of the 3 regular and 8 semi-regular tessellations, but this is not
a very precise definition. Others have tried for more specific or complicated
definitions. If you're interested in finding out more you can read
a description of polymorph
tessellations here.

And some people allow for tessellations of curved shapes.

The above exampe of the tessellated lizards was done by famous artist MC Escher.