Tessellation Shapes and Math in Tessellations

Not all polygons are tessellation shapes. A tessellation is a collection of figures that can be put together to fill a plane surface without overlaps or gaps. I’m sure that you have already seen many tessellations in real life. The tiles in the kitchen and the puzzle you have solved are nothing but tessellations.

Let’s talk a little about the math in tessellations. If you want to cover the plane with regular congruent polygons, you are trying to create a regular tessellation. This type of tessellation can not be achieved with any type of polygons.

Regular polygons have all sides and all angles congruent. The equilateral triangle, the square, the regular pentagon are all examples of regular polygons. Did you know that you cannot create a tessellation with regular pentagons? Or with regular octagons? As a matter of fact there are only three types of regular polygons that can be used to make regular tessellations.

They are:

• The equilateral triangle
• The square
• The regular hexagon

In the following video you can see how easy it is to create a tessellation with these types of regular polygons:

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