Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps. Remember the last puzzle you put together? Well, that was a tessellation! The shapes were just really weird.

Example:

We usually add a few more rules to make things interesting!

REGULAR TESSELLATIONS:

• RULE #1:   The tessellation must tile a floor (that goes on forever) with no overlapping or gaps.
• RULE #2:  The tiles must be regular polygons - and all the same.
• RULE #3:   Each vertex must look the same.

What's a vertex?

where all the "corners" meet!

What can we tessellate using these rules?

Triangles?   Yep!

Notice what happens at each vertex!

The interior angle of each equilateral triangle is 
60 degrees.....

60 + 60 + 60 + 60 + 60 + 60 = 360 degrees