# A LITTLE EASY GEOMETRY:THE BASICS OF TESSELLATION

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How to make a tessellation? Well, your tessellation must be based on a basic shape that can tessellate. Look at the brown fox picture on this page. Can you see the regular geometric shape they are based on? If you'd like to see that basic shape revealed, just let your mouse cursor hover over the fox picture for a moment.

A parallelogram is that picture's fundamental, or primary, cell. In tessellation art, the "cell" is the basic tessellating shape a "tile" is based on. Said simply, a "cell" is the basic tessellating geometric shape that an artist started with when creating a tessellation. A "tile" is the repeated shape in the picture. In our example, a fox is a "tile".

Parallelograms are basic geometric shapes-- "cells" that will always tessellate. So will some triangles, and all hexagons.

You can see that every part needed to make up the full fox picture at left is contained in the parallelogram. All you need to do is to repeat the "tiles" and you get the full tessellation. By joining similar points in a tessellation, it should usually be possible to work out the fundamental tile's shape. As you look at the art on this website, can you see whether the tiles are based on tweaking the shapes of parallelograms...or triangles...or hexagons?

In 2-motif (two tile) tessellations the art will contain two basic tile shapes! Click here to see an example, my "hawks and horses" picture. For another example, imagine octagons (8-sided shapes) pressed together, with smaller squares filling the gaps between the octagons. Octagons-plus-squares is a basic kind of 2-motif tessellation. For yet another example, look at a soccer ball. Can you see the 2-motif tessellation on it? What shapes are the 2 kinds of tiles on a soccer ball?

Can you find or imagine a tessellation with 3 or 4 or 5 motifs (3 or 4 or 5 tile shapes)? They exist. Show us some! I'll post the best of them on this website.