Classification and generation of nanocones

Nanocones are carbon networks that can be modeled as infinite cubic plane graphs with 1≤p≤51≤p≤5 pentagons and all the other faces hexagons. In this paper, we give a short proof of the fact that nanocones fall into eight classes when classified according to isomorphism up to a finite region, and describe a finer classification taking the localization of the pentagons into account. For this finer classification, we also describe an efficient algorithm to enumerate all non-equivalent nanocone representatives for a given parameter set, and give results of an implementation of the algorithm.

► We give a short proof of the fact that nanocones fall into eight equivalence classes.
► We give a finer classification with respect to the localization of the pentagons.
► We describe an efficient algorithm to enumerate all non-equivalent nanocones.
► We present the results of a program based on this algorithm.