Tessellations

Trevor's blog got me thinking about patterns, and specifically, tessellations. But before I started writing this blog, I knew very little about tessellations. I only knew that they were pretty, so I decided to do some research. Here is what I found:

In a tessellation, all of the shapes must meet around a common vertex. So that means that this:  isn't a tessellation because the shapes don't all meet at one corner.


I also learned that there are four different types of tessellations. There are regular tessellations, made of a congruent, regular shape repeating. There are only three different regular tessellations, the triangle, square, and hexagon. This is because these are the only shapes whose angles are multiples of 360. At the vertex, the angles all add up to 360. 

The next type of tessellation is the semi-regular tessellation. This has the same regular shapes repeating, but there can be more than one shape. There are only 8 of these. 

The next type of tessellation is the nonuniform, periodic tessellation. This has a pattern, but the shapes meeting at the vertices can all be different. There are an infinite number of these tessellations.

The last type of tessellation is the nonuniform, non-periodic tessellation. This tessellation does not have any specific pattern. 

Finally, I looked up images of tessellations. Here are some of my favorites: