# Tiling the Plane.

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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.â€‹
• Use the red circle to rotate the figure.â€‹
• With the slider now at 4, move the figure to tesselate the plane.â€‹
• 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 doesnâ€™t.)

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Which Regular Plane Figures Tile a Plane?

• Move the “vertices” slider in the applet below to start at 3.â€‹
• Use the red circle to rotate the figure to form a tessellation. Any direction you choose is ok.â€‹â€‹
• 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.

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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.

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