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Buckyball Lattice

A pure-carbon structure, with a structure like a soccer ball.

In Brief

Carbon is the most versatile of the elements, combining in an apparently endless variety of configurations. In 1985, scientists at Rice University discovered a compound with the chemical formula C60. Now what kind of geometry did it have?

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The shape is a truncated icosahedron.

The scientists named this class of compounds “fullerenes”, and this particular one “buckminsterfullerene”, after the inventor Buckminster Fuller. The carbon-carbon bonds that separate two hexagonal faces are drawn in gold; bonds that separate a hexagon and a pentagon are blue.

There is an interesting connection between this shape and the golden ratio φ: the coordinates of the vertices are (0, ±1, ±3φ), (±1, ±3φ, 0), (±3φ, 0, ±1), ...yes, it goes on. For the full story, just look at the HTML source of this page.

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