Tessellations

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

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.

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.

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

Examples of Tessellations

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

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