## Buckyballs Detected in Space

For the first time, scientists have verified the existence of “buckyballs” in space. Buckyballs are carbon molecules made up of 60 atoms arranged in a soccer-ball like structure

Notice the interlocking pentagons and hexagons. There are 60 vertices in this solid, so how many of each polygon?

Buckyballs are named after Buckminster Fuller, as they resemble the geodesic dome he made famous. Fuller was a creative, prolific man–**a futurist**–who was never short of whimsical ideas, like using blimps to drop bombs to make holes to plant tree-houses in.

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I counted 12 pentagons and 20 hexagons. Counting each vertex of these 32 polygons gives a total of 12×5 + 20×6 = 180 vertices. But each vertex of the buckyball is part of 3 polygons (not that it matters, but it’s always 2 hexagons and 1 pentagon), so 180/3 gives the 60 total vertices.