Prediction of the number of carbon atoms in various nanostructures by using geometrical approach

With the growth of nanotechnology, many attempts have been made on the chemical and physical properties of nanostructures. Due to relation between physical properties and geometrical structure, understanding of the geometrical structure is very important. Moreover, this can be useful for finding unknown structures that have not been produced in laboratory yet. In the present work, first we have investigated the structure of some nanostructures from the geometrical point of view. Then an algorithm is proposed for discovering the number of carbon atoms in various nanotubes and fullerenes. In the presented algorithm, a nanosheet in 2D space is considered as a start point. Creating twelve nanocones in nanosheet makes it a nanostructure. Different nanostructures are produced by relocation of nanocones. The result shows that the number of carbon atoms in different nanostructures is a sequence that has infinite harmonies and follows a simple formula. Each harmony is an arithmetic progression.