Fusion reactions of cages and fullerenes C4, C6 C8, C10, C12 and C14 with each other are modeled on the basis of Arrhenius's postulate. It means that at first there forms an intermediate compound and afterwards a chemical reaction is going on. During the reactions new covalent bonds between the reacting atoms of different fullerenes are formed and old covalent bonds are destroyed. The process is similar to fusion of bubbles in a soap solution. The graphs describing the process are suggested. We have obtained fullerenes C8, C12 C16, C20, C24 and C28 that can be incorporated in the fullerene periodic system as the Δn=4 series.