Totally Tessellated: To Main Page
History and Culture of TessellationsEssential Information Regarding TessellationsMosaics/TilingsM. C. Escher and His Unique Approach to TessellationsBeyond the Basics of Tessellations
Toolbar
Beyond the Regular, Semiregular,
and Demiregular Tessellations

Demiregular tessellations limit the number of different polygon arrangements to exactly two or three. If we remove this limitation and consider tessellations of regular polygons with more than three different polygon arrangements, the number of possibilities becomes infinite.

Here is an example:

Example of a Tessellation of Regular Polygons with Four Different Polygon Arrangments

There are four different polygon arrangements: around vertex 1 is 4.6.12, around vertex 2 is 3.3.4.12, around vertex 3 is 3.3.3.3.6, and around vertex 4 is 3.4.4.6. We could name this tessellation 4.6.12 / 3.3.4.12 / 3.3.3.3.6 / 3.4.4.6

 

Here is another example even more complex than the last:

Example of a Tessellation of Regular Polygons with Six Different Polygon Arrangments

There are six different polygon arrangements: around vertex 1 is 3.6.3.6, around vertex 2 is 3.4.4.6, around vertex 3 is 3.4.6.4, around vertex 4 is 3.3.4.12, around vertex 5 is 3.3.3.4.4, around vertex 6 is 4.4.4.4. We could call this tessellation 3.6.3.6 / 3.4.4.6 / 3.4.6.4 /3.3.4.12 / 3.3.3.4.4 / 4.4.4.4

 

As you may see, we can increase the complexity of our tessellations of regular polygons as much as we wanted. For example, we can always make the tessellation design larger and more complex. Try creating some unique ones of your own!

TemplatesFor templates of regular polygons that you can print and cut out, proceed to the templates page:

top of the page