Shapes That Tessellate

Instructor: Mary Beth Burns

Mary Beth has taught 1st, 4th and 5th grade and has a specialist degree in Educational Leadership. She is currently an assistant principal.

Tessellations can be very mesmerizing to look at, and they are actually a part of mathematics! Come and learn about what tessellations are, which shapes are able to tessellate, and which shapes are not able to do so.

What Is a Tessellation?

Let's pretend that you found a beautiful tree house in your backyard. It has glass windows and the walls are painted your favorite color. There's only one problem: whoever built the tree house forgot to put a floor in! A dirt floor simply will not do in this beautiful tree house, so you have decided to buy some tile and create a beautiful tile floor.

You will need to tap into your tessellation skills in order to get the job done. In fact, tiling and tessellation are synonyms, which means that they mean the same thing. In order to make a tessellation, you need many copies of a shape. That shape is repeated over and over, which makes a type of patterned design. An important element of tessellations is that they don't have any overlaps or gaps. You wouldn't want the dirt floor to show through, would you?

In math, you will most likely learn about tessellations in a geometry class. Tessellations are made of shapes, and shapes are a huge part of geometry. Tessellations can be made infinite, meaning that they have no end. The pattern can continue on and on into eternity!

Shapes that Tessellate

There are three shapes that are able to tessellate all by themselves, and one of them is the square, which is kind of obvious. In fact, the square was the first shape to ever be tessellated! This would also be a good choice for tiling that dream tree house. You could buy several square tiles and they would fit right against one another, making a tessellation.

The other two shapes that can tessellate all by themselves are triangles and hexagons. In order for the tessellation to work, the shapes must be congruent, or identical; if you had triangles that were all different sizes, they would not tessellate.

A triangle tessellation
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You can also make a special kind of tessellation with a variety of different shapes. This is known as a semi-regular tessellation. For example, you can use a combination of hexagons, triangles and squares to make a beautiful semi-regular tessellation.

A semi-regular tessellation
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