# Bridges 2010 Short Paper

Constructing Molecules with Beads: The Geometry of Topologically Nontrivial Fullerenes

Bih-Yaw Jin, Chern Chuang and Chia-Chin Tsoo

(Proceedings pages 391–394)

## Abstract

Three-dimensional molecular structures of topologically nontrivial
fullerenes (consisting of either finite or extended structures) are
usually aesthetically pleasing. In this article, we demonstrate
that beads such as the ones commonly used in decorative art and
ornament making can also be used to construct arbitrary fullerene
structures. Based on the spiral codes of fullerenes, we developed
a systematic strategy for making physical models of cage-like
fullerenes use common beads. The resulting beaded model structure
is similar to the true three-dimensional molecular structure of
corresponding fullerene due to an interesting analogy between the
hard-sphere repulsion among neighboring beads and the microscopic
valence shell electron pair repulsion for the sp^{2}-hybridized
carbon atoms. More complicated fullerenes models that have nontrivial
topology (e.g. toroidal carbon nanotubes, helically coiled carbon
nanotubes, and high-genus fullerenes) can also be faithfully
constructed using beads. Beaded models of extended graphitic
structures such as those that correspond to tiling of graphene sheet
on a Schwartz P- and D- surfaces, Shoen I-WP, and Nervious surfaces,
can also been created.

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