1. Tessellations

2. A Tessellation is a collection of figures that cover a plane with no gaps or overlaps. You can use transformations to create them.

3. On the left is a true tessellation; on the right is not a tessellation but a pattern.
Patterns repeat but do not have clearly defined closed shapes.
Tessellations repeat and do have clearly defined closed shapes.

4. A pure tessellation consists of congruent copies.
THERE are only three regular polygons that makeup a pure tessellation!
What are they?
Remember: Regular means that the sides and angles of the polygon are all the same length.
If polygons do not have to be regular, then there are many that will tessellate a plane.
For example: any triangle or any quadrilateral will tessellate.

5. Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons. We can't show the entire plane, but imagine that these are pieces taken from planes that have been tiled. Here are examples of
a tessellation of triangles
a tessellation of squares
a tessellation of hexagons

6. Examples of Tessellations

8. Here are a few sample tessellations created by famous Dutch artist M. C. Escher

9. These regular polygons can be transformed to create more complicated tessellations.
Lets see how this can work:
Let’s
Tessellate