If you chop the corners off an icosahedron, you are left with 20 hexagon faces and 12 pentagon faces. The model below is constructed with just the hexagons (drag with your mouse to move it):

The truncated icosahedron is commonly known as a buckyball, after the guy who discovered a structure of carbon with atoms arranged as a truncated icosahedron. It is also used for footballs:

(Java applet from LiveGraphics3D)


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