Math Monday: Know Your Truncated Icosahedron

Glen Whitney

Executive Director, Museum of Mathematics

39 Articles

By Glen Whitney

Executive Director, Museum of Mathematics

39 Articles

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For the Museum of Mathematics


Take an icosahedron, say one made out of something soft, like chocolate, and slice off each of the corners:

You get a structure called (rather prosaically) a truncated icosahedron. Here’s one rendered in wood (by artist Ai Weiwei):

This structure is also known as a soccer ball:

Or a buckminsterfullerene:

Continuing the Buckminster Fuller theme from last time, today’s column is devoted to notable truncated icosahedron constructions. This polyhedron has been used in an incredible variety of ways for decades.

First, there is the 1949 Autonomous Living Unit by Fuller himself:

The great circles intersecting the faces of this structure make the truncated dodecahedron a bit hard to see, but it’s there: one of the pentagons is front and center, just above the white prism that may serve as the unit’s front door.

Second is the optional hub cap of the Pontiac Trans Am, years 1971-76:

Third, featured at the 2012 New York City Maker Faire, New York Hall of Science, was the rotating Happy Fun Ball by Rob Marshall:

And finally, perhaps the most dramatic truncated icosahedron (or pair of them) yet, is Leo Villareal’s Buckyball, which was on display in Madison Square Park in Manhattan in 2012.

The striking edge lighting changes through a myriad of patterns: