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).
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.