This is a
picture of C60 buckminsterfullerine or a bucky ball. If you would like
to see a buckyball that you can rotate click here
This is a
picture of C60 buckminsterfullerine or a bucky ball. If you would like
to see a buckyball that you can rotate click here
Natural carbon can exist in several forms. Most people know about graphite and diamond, but there is a third type-- fullerenes. Sometimes these are mistakenly called a "new form of carbon"; in fact, fullerenes have been found to exist in interstellar dust as well as in geological formations on Earth. They are only new to us. Fullerenes are large carbon-cage molecules. By far the most common one is C60-- also called a "buckyball"-- but some other relatively common ones are C70, C76, and C84 (there are plenty of others too). In 1996 the Nobel prize was awarded to the 3 people who had discovered fullerenes. If you would like to know more about the uses of fullerenes see here
The mathematical name for the C60 buckyball is the truncated icosahedron. An icosahedron is the one of the five Platonic solids (3-D shapes whose faces are identical regular polygons). It has 20 faces, each one an equilateral triangle. The other four are the tetrahedron, the cube, the octahedron, and the dodecahedron. If you would like to know more about the platonic solids then click here
Chopping off each vertex reveals the 12 pentagonal and 20 hexagonal faces of the truncated icosahedron, which is one of the 13 Archimedean solids (shapes made from truncating Platonic solids in certain ways, for more details see here). The process is shown below:
This object is highly symmetric, and is actually the shape that most modern footballs are made in, as it is such a good approximation to a sphere, yet it is made of easy to cut flat shapes.
You can make your own model of a buckyball. Just print out the figure
below, cut around its edge, and start folding along the lines common to
2 hexagons. You will find that the flat sheet neatly curls up into a
sphere-like object as rings of hexagons are connected by pentagons
(really, this is easy, the figure practically makes itself once you
start folding). The spaces allow the sheet to generate pentagons as you
are rolling, so all parts shown are hexagons. Carbon is normally found
in two other forms diamond and graphite. Graphite is formed out of
sheets of carbon joined into hexagons. With some bonds missing the
graphite sheet can roll up into a buckyball-- a few pieces of tape, and
you'll have your own truncated icosahedron. Enjoy! 
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