Density Functional Theory has been used to model the Diels-Alder reactions of the fullerene fragments triindenetriphenilene and pentacyclopentacorannulene with ethylene and 1,3-butadiene. The purpose is to prove the feasibility of using Diels-Alder cycloaddition reactions to grow fullerene fragments step by step, and to dimerize fullerene fragments, as a way to obtain C60. The dienophile character of the fullerene fragments is dominant, and the reaction of butadiene with pentacyclopentacorannulene is favored.