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Semi-regular Tessellation: Definition & Examples

Instructor: Mark Boster
Often adults will tell you things over and over. 'Look both ways before crossing the street.' ' Don't get in a car with someone without my permission.' and 'Eat your vegetables.' Well, just like your parents, semi-regular tessellations repeat too!

Tessellations in Real Life

Barry has five brothers and sisters. All six siblings asked their mother if each one of them could have a cookie. There were only five cookies. That meant that one person wasn't going to get a cookie.

Barry said he would trade his cookie for one dollar. A dollar is a lot for a cookie, but one of his brothers gave it to him anyway. Why did his brother pay so much for a cookie? Well, there weren't many of them, so each one was very important, just like semi-regular tessellations.

Have you ever heard of semi-regular tessellations? Well, there are only eight of them, so just like the cookies, they must be important, too, right?

Tessellations

A tessellation is a pattern of a shape or shapes in geometry that repeat. There are as many tessellations as you can imagine.

An Example of a Tessellation
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Semi-Regular Tessellations

A semi-regular tessellation is made up of two or more regular polygons that are arranged the same at every vertex, which is just a fancy math name for a corner. A regular polygon is a polygon where all the sides and angles are the same. All of the polygons in a semi-regular tessellation must be the same length for the pattern to work. As we said earlier, semi-regular tessellations are special because there are only eight of them.

Spotting Semi-Regular Tessellations

Let's look at an example of a semi-regular tessellation.

A Semi-Regular Tessellation
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First, identify the types of polygons in the pattern. There are regular triangles (shown in green) and regular hexagons, or 6-sided figures (shown in grey). So far, the definition of a semi-regular tessellation is working because there are at least two regular polygons. Now, see if they are arranged the same way at every vertex and if all of the sides of all of the shapes are the same length.

Next, pick any vertex or corner. There is one marked for you. Count the sides of the shapes around that point.

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