Quadrilateral Tessellations with GeoGebra

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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

  1. Go to http://www.geogebra.org/webstart/geogebra.html to load a web-based applet version of GeoGebra.
  2. Go to the View menu and unselect the "Axes" and "Algebra View" options. You should now have just a blank window to work with.
  3. Use the "Polygon" tool to draw a quadrilateral.
  4. Construct the midpoints of all four sides of the quadrilateral.
  5. 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.
  6. Your picture should look something like this:

    QuadTessGeoGebra.jpg
  7. Use translations to finish the tessellation.
  8. Move the corners of the original quadrilateral. Examine what happens when it is not convex. Do you still have a tessellation?
  9. 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.
  10. What symmetries does the picture have? What symmetry group does the tessellation have?
  11. If you change the original quadrilateral, what other groups can you achieve?