How to Make an Icosahedron With Toothpicks
An icosahedron is a polyhedron that has 30 sides, 20 faces and 12 vertices, or points. Each face is an equilateral triangle. Buckminster Fuller, who popularized the geodesic dome, based his original design on the icosahedron. Fuller and others also produced world maps based on many forms of polyhedra, including the icosahedron. You can quickly construct a small model of an icosahedron with some very simple materials that you may already have at home.
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Instructions
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Make a pentagon by placing five toothpicks into five small balls of clay in a ring to create a five-sided shape.
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Make a second identical pentagon.
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Place two toothpicks into each ball of clay on one of the pentagons, angling them so that they form equilateral triangles all the way around the pentagon. The triangles should be sticking up at a 90-degree angle from the pentagon. In other words, your pentagon is laying flat on the table, and the triangles are sticking straight up in the air.
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Attach the second pentagon to the top of the triangles. There will be two toothpicks to stick into each piece of clay. Now you will have two pentagons attached by triangles.
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Place five more toothpicks into the balls of clay (one toothpick per ball) around the top pentagon, and bring all five toothpicks to a point above the center of the pentagon, securing them all together with one more ball of clay.
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Repeat on the bottom pentagon with five more toothpicks and one more ball of clay.
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