Tiling the Plane.

AIM: Do all plane figures tile a plane?

  • With the slider at its default position, n = 3, move the blue triangle by holding the white circle to tesselate the plane.
  • Use the red circle to rotate the figure.
  • With the slider now at 4, move the figure to tesselate the plane.
  • Repeat the steps with n taking different values up to 10 .
  • Complete the following table; (Yes if it tiles the plane, and No if it doesn’t.)

AIM: Which regular plane figures tile a plane?

  • Move the “vertices” slider in the applet below to start at 3.​
  • Use the red circle to rotate the figure to form a tessellation. Any direction you choose is ok.​​
  • Repeat the steps with different number of sides up to 15. (Note: For tiling to occur, there must be no gaps or overlaps.)

From the activity above, the triangle, square, and hexagon are the only polygons that will tile the plane.

AIM: Can different shapes be jointly used to tile the Plane ?

  • Move and rotate the tiles by holding the red points to create a design.

Play around with the polygons and observe which ones could be used jointly to create a nice pattern for your floor or rug.