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. Describe the symmetries of the “Lizards” tessellation.

2. What is the tessellation’s underlying polygonal structure

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Move Sliders Alpha and Beta:

3. What shape is the tile formed from? What specific transformation could be used to move the tile into the spot of another lizard? How was the tile formed?

Duke, 11/01/06, Created with GeoGebra