The icosahedron – 4


When you truncate the icosahedron (in other words, you divide each edge of each triangle in thirds, and then cut off each of the tips of the icosahedron to the 1/3 mark), you get a polyhedron called the truncated icosahedron (commonly known as the Buckyball). It has 12 pentagons, each surrounded by hexagons.

Tuncated icosahedron #1 Tuncated icosahedron #2 Tuncated icosahedron #3

2-D honeycomb that can be folded up into a 3-D truncated icosahedronThis, of course, is the shape of a soccer ball. It's also the 3-D shape you would get if you were to take a 2-D honeycomb of 32 hexagons, slice a pie-shaped piece out of twelve of the hexagons, and then fold them up to make pentagons.

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