http://www.ck12.org Chapter 12. Rigid Transformations
This is the final tessellation. You can continue to tessellate this shape forever.
Now, continue to fill in around the figures with either the original or the rotation.
Example 2:Does a regular pentagon tessellate?
Solution:First, recall that there are( 5 − 2 ) 180 ◦= 540 ◦in a pentagon and each angle is 540◦÷ 5 = 108 ◦. From this,
we know that a regular pentagon will not tessellate by itself because 108◦× 3 = 324 ◦and 108◦× 4 = 432 ◦.
For a shape to be tessellated, the angles around every point must add up to 360◦. A regular pentagon does not
tessellate by itself. But, if we add in another shape, a rhombus, for example, then the two shapes together will
tessellate.
Tessellations can also be much more complicated. Here are a couple of examples.