The new shapes belong to  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.

Below we see how the new shapes can more closely approach a spherical shape than classical fullerenes (right):

— MOLECULAR GRAPHICS PERFORMED WITH THE UNIVERSITY OF CALIFORNIA, SAN FRANCISCO CHIMERA PACKAGE. FIGURE PROVIDED BY S. SCHEIN

The new shapes:

- Are convex, which means they do not have parts that are caved in,

- they do not have equal angles but they do have equilateral edges (meaning each edge is the same length), and

- all of their faces are “planar”, which is very important, meaning that the faces lie flat and do not bulge in or out.

Stan Schein (left) and James Gayed are not mathematicians, but they are polyhedron lovers:

—PHOTO CREDIT ALEX YEH

Below, some examples of these new forms —which are a modification of a previously known class of cages called Goldberg cages:

Find out more with these two great articles: 

Science News

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