Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. You can have other tessellations of regular shapes if you use more than one type of shape.

Why does a square tessellate?

Squares, for example, have four angles that are 90 degrees. So, here's the trick: the angles must be a divisor of 360 degrees in order to tessellate. 360 divided by 90 = 4; this is why squares are able to tessellate.

What shapes can tessellate?

Only three regular polygons (shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons. What about circles? Circles are a type of oval—a convex, curved shape with no corners.