# Quadrilateral Tessellations with GeoGebra

From EscherMath

**Objective:**
Use GeoGebra to create a tessellation with quadrilaterals. Doing the construction on the computer allows you to change the shape of your original quadrilateral and see how the tessellation changes.

Note: Some of the basic tools used here are explained in more detail in Triangular Tessellations with GeoGebra

- Go to http://www.geogebra.org/webstart/geogebra.html to load a web-based applet version of GeoGebra.
- Go to the View menu and unselect the "Axes" and "Algebra View" options. You should now have just a blank window to work with.
- Use the "Polygon" tool to draw a quadrilateral.
- Construct the midpoints of all four sides of the quadrilateral.
- Rotate the quadrilateral 180° around each midpoint. Color all four new copies with one color. To do this hold the CTRL key and click (right click on a PC) on each of the new quadrilaterals to bring up a menu. The bottom option is "Object Properties." Click on it and then select the color tab.
- Use translations to finish the tessellation.
- Move the corners of the original quadrilateral. Examine what happens when it is not convex. Do you still have a tessellation?
- Add your name to the sketch using the Text palette. Save it to the desktop and email it to yourself so you can print it later.
- What symmetries does the picture have? What symmetry group does the tessellation have?
- If you change the original quadrilateral, what other groups can you achieve?

Your picture should look something like this: