Beyond Triangles, Squares, Pentagons, and Hexagons

At this point, we have already seen numerous ways to modify tessellations ranging from three to six-sided polygons. Although tessellations of hexagons stretches the limits of tesselations, it is still possible to discover special types of polygons with more than six sides that will tessellate.

For example, consider the following nonagon (nine sides). It was created from a pentagon using a technique that we have already seen. The dotted line indicates an original side of the original pentagon. Notice how this side was divided into halves and how one half became a pattern that was rotated to replace the other half. The resulting shape tessellates in a predictable manner (similar to ones we have already seen).

 A technique for creating a nonagon that can tessellate. Note how similar it is to Limited Technique 3 for pentagons and Limited Technique 2 for hexagons.

The following example is a tessellation that can be created using the concept of unit cells. The important idea is that we have enough techniques (e.g., division) to indirectly create tessellations of polygons of more than six sides. Therefore, directly investigating polygons with more than six sides may not be necessary.

 Here is a nonagon (nine-sided polygon) that can tessellate. This tessellation can be created using the concept of unit cells. (The unit cell in this example is the equilateral triangle which is repeated throughout the tessellation.)