What is a Tessellation?

A tessellation can be made from polygons which are closed plane figures with more than two sides. By "closed plane," that means the shape is one that can lie flat on a plane surface, and where there are no openings in the shape--the sides join together to form one "piece".

Tessellations have many interesting mathematical properties. You can experiment with the area and perimeter of your polygons using this activity. Click on the 'Information' button to find the area and perimeter of your shape. Can you make a shape with a larger perimeter? With a larger area?

Tessellations can also take on very different appearances based on how they are colored. Try changing the colors of your tessellation to see how the shapes appear.

You may notice that our brains play an important part in how we perceive objects. For example, take a look at this tessellation and describe what you see:

It is an example of an optical illusion: something that appears to our eyes to have an effect that it does not really have. The placement of the alternating dark and light squares "tricks" our eyes into seeing the horizontal lines as crooked.

Tessellations also display Plane Symmetries. See if you can make tessellations with these types of symmetry:

Reflection - If you were to fold over your tessellation would the same shape appear?
Translation - If you could slide the tessellation, would it appear the same.
Rotation - If you rotate the tessellation around an axis, does the same pattern appear?
Glide Reflection - If you slide your tessellation across the plane and then flip it over, is it the same?

See Examples of Plane Symmetry in Tessellations.

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