Demiregular Tessellations (1/2)

 1. General Information 2. The Demiregular Tessellations
General Information
The definitions of regular and semiregular tessellations are limited. To refresh your memory, regular tessellations must be composed of only one regular polygon, and semiregular tessellations must have the same polygon arrangment at each and every vertex of the design. However, let us extend beyond this limited definitions. What if we allow different arrangements of regular polygons at the vertices of a tessellation? Here is a simple example:

 The arrangement at vertex 1 is 3.6.3.6, while the arrangement at vertex 2 is 3.3.6.6

This is still a tessellation consisting of regular polygons. The reason that this is not a regular nor a semiregular tessellation is that there are two types of vertices which we identify as 3.6.3.6 and 3.3.6.6.

Similar to how we named the regular and semiregular tessellations by their polygon arrangments, we name this new tessellation by listing the types of polygons arrangements separated by a "/" symbol. Thus, the above tessellation is 3.6.3.6 / 3.3.6.6.

Mathematicians have defined demiregular tessellations as tessellations of regular polygons in which there are either two or three different polygon arrangements. There are at least 14 demiregular tessellations. How was this determined? The process is almost fully trial-and-error and just requires a lot of time and effort.

 A real example of a demiregular tessellation:

 To browse full-page templates of the demiregular tessellations that are ready to be printed, proceed to the templates page: