Tessellation
A Tessellation (or Tiling) is when you cover a surface with a pattern of flat shapes so that there are no overlaps or gaps
Examples:





Rectangles


Octagons and Squares


Different Pentagons

Regular Tessellations
A regular tessellation is a pattern made by repeating a regular polygon. There are only 3 regular tessellations:





Triangles


Squares


Hexagons

3.3.3.3.3.3


4.4.4.4


6.6.6

Look at a Vertex ...

A vertex is just a "corner point".
What shapes meet here?


Three hexagons meet at this vertex,
and a hexagon has 6 sides.
So this is called a "6.6.6" tessellation.




For a regular tessellation, the pattern is identical at each vertex!

Semiregular Tessellations
A semiregular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same! There are only 8 semiregular tessellations:





3.3.3.3.6 

3.3.3.4.4 

3.3.4.3.4 










3.4.6.4 

3.6.3.6 

3.12.12 










4.6.12 

4.8.8 







Other Tessellations
There are also "demiregular" tessellations, but mathematicians disagree on what they actually are!
And some people allow curved shapes (not just polygons) so you can have tessellations like these:





Curvy Shapes


Circles


Eagles?

Tessellation Artist
All these images were made using Tessellation Artist, (with some color added using a paint program).
You can try it too  maybe you will invent a new tessellation!
