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{\large \textbf{Fullerene Symmetries and Coxeter Groups Approach}}



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{\large Maia Angelova\smallskip }



maia.angelova@unn.ac.uk\medskip



School of Computing and Mathematics\smallskip



University of Northumbria at Newcastle



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{\large \textit{Abstract}}



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Fullerenes, $C_{n}$, are all-carbon molecules with a closed-cage
structure and a nearly spherical appearance. Each carbon atom is
bonded to three others to form a polyhedron with 12 pentagonal and
$\left( \frac{1}{2}%
n-10\right) $ hexagonal faces. The  best known fullerene is
$C_{60}$, the molecule with 60 equivalent carbon atoms arranged on
the vertices of a truncated icosahedron. The properties of $\
C_{60}$  molecule   are discussed and its icosahedral symmetry is
described. Finite Coxeter groups $H_{3}$ and $H_{4}$ and their
Coxeter diagrams are introduced and the symmetry of $C_{60}$
fullerene  is illustrated by the diagrams of
the group $%
H_{3}$. $\;$The solid form of $C_{60}$ is described,
some interesting doped structures are given and their properties
discussed. The symmetries of other popular fullerenes are also
considered. Possible embedding of fullerenes to form onion-like
structures are discussed and illustrated by the groups $H_{3} $
and $H_{4}$.

\bigskip Special knowledge of the matter is not
required. All structures would be illustrated in details and all
necessary definitions given. The talk would be accessible to a
broad audience. \end{document}
