Goldberg variations: New shapes for molecular cages

Flat hexagons and pentagons come together in new twist on old polyhedra

By Dana Mackenzie, 12:21 PM February 14, 2014

In the latest verse of a centuries-old mathematical refrain, scientists have figured a way to iron out the wrinkles in a large class of molecular cages. The cages have faces consisting of 12 regular pentagons and up to 480 irregular hexagons, which puts them into a well-known category of shapes called fullerenes. However, unlike most previously known fullerenes, the new shapes’ hundreds of faces are flat rather than warped, and the atoms in the molecule are equally spaced.

The shapes’ flat fac...

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