Fusion reactions of cupola half-fullerenes C16, C18, C24, C30 and C36 with each other are considered on the basis of Arrhenius's postulate. It means that at first there forms an intermediate compound and only afterwards a usual chemical reaction is going on. The final structure of fullerenes is obtained with the help of geometric modeling and is optimized through the use of Avogadro package. In general, the fullerenes which tend to take the appearance of a perfect spheroid have lesser formation energy. The energy of fullerenes C32, C36, C48, C60 and C72 obtained is calculated. The periodic system of basic perfect fullerenes is suggested.