Escher's "Lizards" Tessellation

 M.C. Escher was the master of transforming polygonal tessellations into non-polygonal works of art. The connection between the symmetries of the underlying polygonal tessellation, and the symmetries of the transformed tessellation can be traced back to the transformations used to create the non-polygonal tile.

Before moving any of the sliders, examine Escher’s "Lizards" tessellation below and answer the following questions:

1.  What is a symmetry transformation?

2.  Describe the symmetries that appear to be in the “Lizards” tessellation.

3.  What is the tessellation’s underlying polygonal structure? (Hint: Locate points where more than two lizards come together.)

4.  What are the symmetries of this underlying tessellation?

Move only sliders Alpha and Beta to their maximums and back again a few times:

4.  Describe how the tile was formed from its underlying polygon? Use precise vocabulary.

5.  Identify the vertices where the tile building transformations are taking place.  Describe their location on the underlying polygon.

6.  What transformation(s) could be used to move the tile into the spots of other lizards?

Move the other two sliders one at a time:

7.  Describe the transformations taking place. Use precise vocabulary.

8.  Discuss how the filling of the plane could be achieved using these transformations.

Duke, 11/01/06, Created with GeoGebra