An array of simple materials ready for transformation. Art is math is sport is science is philosophy is great design.
Begin by creating templates for the hexagons and pentagons. For this model, each edge measures 3 3/4 inches. In some classes, I have them actually draft each shape using compasses, rulers, and mathematics. But this time, we just created and traced the templates.
The next task: to determine how many hexagons/pentagons you can get on the posterboard. We didn’t want to waste any paper! It did not take long to figure out what the tile pattern had to be in order to get 9 hexagons on each sheet (the maximum possible). All pieces have to be precisely cut.
Cutting takes some practice, but we all help each other out until every student has a total of 32 pieces.
Another pattern emerges as we begin to construct the polyhedra.
Bit by bit, the room fills up with completed models.
This polyhedra is called a truncated icosahedron. I chose this particular model to build to honor the world cup fever that is sweeping the classroom these days. Finished product: fabulous! A room full of these hanging from the ceiling is an amazing sight. The equation V-E+F=2 applies to all regular polyhedron. This formula was worked out by Euler in the 1700’s and has been pondered ever since. V=vertices, E=edges, F=faces. The truncated icosahedron has 60 vertices, 90 edges, 32 faces. Do the math! http://www.korthalsaltes.com/ for more templates and interesting projects.
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