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A Teacher's Guide to Building the Icosahedron as a Class Project

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Cutting the template

After you have decided the length of an edge of your icosahedron, you will need to cut 20 identical equilateral triangles from the foamboard. For large triangles, it may be difficult to construct an equilateral triangle since it is hard to find sufficiently large compasses. You can either create a makeshift compass out of cord, a thumbtack, and a pencil (see Figure 4), or you can use a protractor to ensure that your triangles all have 60 degree angles. Use the straightedge to help you cut along a straight line.

You can also use a copying machine to blow up a picture of an equilateral triangle. A portion of a triangle with 9 inch sides is represented in Figure 5 (it is to large to display on this page).

One hint that worked well for us: take a piece of "mat board" (also available from art supply stores for a few dollars) and spend a lot of time cutting one (nearly) perfect equilateral triangle and punching holes in the appropriate places. (Poster board would also work; it is cheaper than mat board, though not as rigid.) Then use this piece of board as a template for cutting the foamboard. That way, every foamboard triangle is exactly the same and you only need to measure one equilateral triangle.

While older students can safely cut their own triangles (assuming you have several X-acto knives), we suggest that the instructor cut all twenty triangles for younger students.

Once twenty equilateral triangles are cut, punch holes into each of the three corners of each triangle. The holes should be about 1/4-1/2 inch inside of each edge (see Figure 6). The hole should be about 1/4 inch in diameter. These holes will be used to connect one face of the icosahedron to an adjacent face. If the side length of your icosahedron is more than 18 inches long, then you will also want to punch a hole at the midpoint of each side of each triangle. This is to prevent the large faces from being too "floppy."

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