Symmetrical Features of the Structure of C₂₄ and C₄₈ Fullerenes

V. M. Talanov^a, N. V. Fedorova^a, and V. V. Gusarov^b,*

^aSouth Russia State Technical University (Novocherkassk Polytechnic Institute),
ul. Prosveshcheniya 132, Novocherkassk, 346414 Russia

^bSt. Petersburg State Institute of Technology (Technical University), Moskovskii pr. 26, St. Petersburg, 190013 Russia

*e-mail: gusarov@hotbox.ru

Received June 2, 2008

Abstract—Structural features of the C₂₄ fullerene and two C₄₈ fullerene isomers with the noncrystallographic
point symmetry group D_6d have been considered. The fundamental domains, Schlegel diagrams, and adjacency
graphs of structural elements of the fundamental domains have been constructed. It has been revealed that all
fullerene faces are pentagons or hexagons but not all of these polygons are regular. The number of pentagonal
faces in all fullerenes under consideration is 12, the number of hexagonal faces in the C₂₄ fullerene is 2, and the
number of hexagonal faces in the C₄₈ fullerenes is 14. The fundamental domains for all the fullerenes under
investigation are not closed because they include the twofold axis of rotation.

Key words: fullerenes, fundamental domain of the point symmetry group, Schlegel diagram, noncrystallo-
graphic point symmetry group, adjacency graph of structural elements

DOI: 10.1134/S1087659610030132

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