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For the Museum of Mathematics

Math Monday banner02 600px Math Monday: Twelve Pentagons, Twenty Hexagons

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

hbgfjehh1 Math Monday: Twelve Pentagons, Twenty Hexagons

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

wooden truncated icosahedron1 Math Monday: Twelve Pentagons, Twenty Hexagons

This structure is also known as a soccer ball:

592 soccer ball p1 Math Monday: Twelve Pentagons, Twenty Hexagons

Or as buckminsterfullerene:

buckminster 0011 Math Monday: Twelve Pentagons, Twenty Hexagons

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 Buckminster Fuller himself:

autonomous1 Math Monday: Twelve Pentagons, Twenty Hexagons

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, model years 1971-76:

71honeycomb1 Math Monday: Twelve Pentagons, Twenty Hexagons

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

mf ride1 Math Monday: Twelve Pentagons, Twenty Hexagons

And finally, perhaps the most dramatic truncated icosahedron (or pair of them) yet, is Leo Villareal’s Buckyball, currently on display in Madison Square Park in Manhattan through 2013 Feb 1.

buckyball nested 1024x7811 Math Monday: Twelve Pentagons, Twenty Hexagons

The striking edge lighting changes through a myriad of patterns:

buckyball jamesewing21 Math Monday: Twelve Pentagons, Twenty Hexagons

It’s auspicious that Buckyball, which links mathematics and culture, will be on display less than 200 meters from the National Museum of Mathematics when it opens soon as America’s primary cultural institution centered on mathematics. We hope to see you in both places!

More:
See all of our Math Monday columns

Glen Whitney

Executive Director, Museum of Mathematics


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