# Chern Chuang

We apply the principles of zome geometry to the construction of complex beaded molecules. Here we put special attention to a family of hypothetical molecules called superfullerenes. They are designed in such a way that each of the atom of a parent molecule (A) is replaced by a buckyball (C60), and the connectivity of the parent molecule is retained in the resulting superstructure (denoted by A⊗C60) by connecting the C60s with straight carbon nanotubes. Both making beaded molecules and proposing reasonable chemical structures require the superstructure to have minimal strain energy. The complexity of this seemingly difficult task can be largely reduced if we make clever use of the properties of zome geometry, that both the C60 and the ball of zometool have icosahedral symmetry and the struts connecting the balls always lie along certain common symmetry axes of the balls. Please see the companion short paper of us for more detailed description.

Straightforward application of this principle to the C60 itself. Thus, this particular example can be seen as a second level Sierpiński structure. It contains 4680 carbon atoms, which translates to 7020 beads. Previously Prof. Bih-Yaw Jin has demonstrated a closely related structure, a C4500 superfullerene, at the 2013 JMM art exhibition held in San Diego. Please refer to the art exhibit archive on the Bridges' website.

This structure is obtained by replacing each of the blue struts of a zometool dodecahedron model with two yellow struts connected through an additional ball, see for example Dr. George Hart's webpage on polyhedra zometool examples. Since the three yellow struts joining at the same ball are too close to each other, we are forced to use C80, which is the second smallest icosahedral fullerene obeying the independent pentagon rule, instead of C60 for the construction scheme to work. In addition to the twenty vertices of a dodecahedron, there are thirty more as the connectors. This structure has 4960 carbon atoms or, equivalently, 7440 beads.