This weekend a couple of my daughters and I put together a buckyball from a Zometool kit. The shape is named for Buckminster Fuller of geodesic dome fame. Two years after Fuller’s death, scientists discovered that the shape appears naturally in the form of a C_{60} molecule, named Buckminsterfullerene in his honor. In geometric lingo, the shape is a truncated icosahedron. It’s also the shape of many soccer balls.

I used the buckyball to introduce the Euler’s formula: V – E + F = 2. (The number of vertices (black balls) minus the number of edges (blue sticks) plus the number of faces (in this case, pentagons and hexagons) always equals 2 for a shape that can be deformed into a sphere.) Being able to physically add and remove vertices or nodes makes the induction proof of Euler’s formula really tangible. Then we looked at 6- and 12-sided dice to show that V – E + F = 2 for these shapes as well.

Thanks to Zometool for sending me the kit.

**Update**: How to show that the Euler characteristic of a torus is zero

**Related post**: Platonic solids

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Hey John, check out vzome.com sometime. It’s free software written by my friend Scott Vorthmann that allows you to play with virtual zome models. You never run out of pieces :) Scott also runs a ‘zomegurus’ mailing list, with entertaining discussion of zome related topics.

I’ve never made a bucky ball, but I have isolated C60 from fullerene enriched soot before. Then I have it to someone as a gift; they’ve probably lost it, sadly. Should have kept it.

They don’t look that impressive though; just like a very, very fine black powder.

Zome is a lot of fun. George Hart (Vi Hart’s dad) has a good book on Zome geometry:

http://www.georgehart.com/zomebook/zomebook.html

An old math grad school friend of mine, David Richter, has a number of Zome Projects on his web site. http://homepages.wmich.edu/~drichter/zomeindex.htm

Looks like fun, but I’m not sure I’d have the patience.

It’s also a truncated dodecahedron, depending on which surfaces you decide to extend.

I love Zomes–I just wish they weren’t quite so expensive. Quality manufacturing, I guess.

And of course it’s also the pattern for a soccer ball. :-)

Nice idea for demonstrating that Euler identity, John.

BTW, I recommend Hugh Aldersey-Williams’s book

The Most Beautiful Moleculefor an illuminating account of the history of the discovery of the fullerenes. It gives an unvarnished account of how science actually works — warts and all.