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
Tessellations of Pentagons (2/3)
 

1. Introduction
2. Limited Technique 1
3. Limited Technique 2
4. Limited Technique 3
5. Hands-On Activities
Limited Technique 2
There is another special of type of pentagon that will tessellate. Any pentagon that has two nonadjacent right angles (90°) and two pairs of sides of equal lengths as indicated in the diagram will tessellate.

A Special Type of Pentagon that Tessellates

The two sides marked with a single hash are congruent, and the two sides marked with a double hash are congruent. Note the two right angles.

 

How do we tessellate this special type of pentagon? The technique takes advantage of the equal side lengths and the convenient 90 degree angles.

Here is one way to visualize this technique:

How to Tessellate This Type of Pentagon

How to tessellate the special type of pentagon; Notice that the right angles all meet at a single vertex

 

Here is a different way to visualize the technique:

How to Tessellate This Type of Pentagon

How to tessellate the special type of pentagon; Notice that the right angles (indicated by blue and red arrows) always meet

 

Both approaches towards visualizing the technique create overall shapes that have parallel and congruent opposite sides. This property allows the overall shape to tessellate an entire plane through a series of simple translations, where opposite sides are lined up.

 

Example Tessellations:
The lightly shaded portions represents the first pattern described above, while the darkly shaded portions represents the second pattern described above. Either portion creates the same tessellation through translations.

 

Up

top of the page