Since their discovery, the fullerenes have challenged scientists with a wide array of problems concerning their properties, behavior, and potential applications. One such fundamental question is that of the assembly of these carbon cages. Much effort has been directed at obtaining an understanding of the process whereby graphite is transformed into fullerenes. In a previous work, we introduced a novel interpretation of the ion chromatography results from fullerene generation experiments. In this work, that interpretation is expanded and ab initio calculations are performed to illustrate how the model explains the experimental results. This "cycloaddition model" is then used to develop a plausible fullerene assembly mechanism.