巨大フラーレンの構造の位相幾何学的考察

抄録

The structures of giant fullerenes have been considered from the topological view point. As the fullerenes are formed of the pentagonal rings and hexagonal rings, Euler's theorem in the topology shows that 12 pentagonal rings are neccessary though the number of hexagonal ones is arbitrary for the formation of the closed polyhedron. This restraint predicts that symmetric giant fullerenes have the following shapes: the icosahedral-shaped, the tetrahedral-shaped, the pentagonal prism-shaped and the hexagonal prism-shaped ones. We have classified the icosahedral-shaped and the tetrahedral-shaped ones into three systems, respectively, and the pentagonal prism-shaped and the hexagonal prism-shaped ones into two systems, respectively, thus totaling ten systems. We have formulated the equations for calculating the number of atoms n in the giant fullerenes C_n. The results indicate that the forming of the round-shaped giant fullerenes requires the sets of heptagonal and pentagonal rings while keeping (the number of pentagonal rings)-(the number of heptagonal rings)=12.