Goldberg variations: New shapes for molecular cages | Science News


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Goldberg variations: New shapes for molecular cages

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

12:21pm, February 14, 2014

SHAPE SHIFTER  A new type of molecular cage has all sides of equal length and flat faces that are all pentagons or hexagons (left). The hexagons have angles that vary from 104 to 142 degrees. A fullerene with the same number of vertices and the same pattern of faces (right) has hexagons with angles that vary in a much narrower range. This forces the hexagonal faces to warp and the cage to assume a pointy shape. 

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 faces make them convex polyhedra, a type of highly symmetric, faceted solid first studied by the ancient Greeks. The first class to be discovered, called the Platonic solids, consists of solids with identical faces that are all regular polygons, meaning shapes with equal sides and angles. There are only five such solids, the most complicated of which is the icosahedron (familiar to game players as the shape of 20-sided dice). A less

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