A systematic search of the regioisomers of the heterofullerenes, C₅₇Pt₂ and C₅₆Pt₂, has been carried out by means of density functional calculations to find the most stable structures. Both heterofullerenes incorporate two metal atoms into the fullerene surface. In the case of C₅₇Pt₂, one platinum atom substitutes one carbon atom of C₆₀ and the other platinum atom replaces a C-C bond, whereas in C₅₆Pt₂ each platinum atom replaces one C-C bond. Several geometric factors were studied, three of which have particularly important effects on the relative stabilities of the regioisomers: the Pt-Pt separation, the number of C-C bonds remaining after substitution, and the type of C-C bond that is substituted. All these factors indicate that the deformation of the carbon framework is a general factor that governs the relative stabilities of the regioisomers. Because a high number of factors affect the stability of the heterofullerenes we also used chemometric techniques in this study. Partial least-squares (PLS) regression was used to establish the structure-energy relationships of C₅₇Pt₂ and C₅₆Pt₂ heterofullerenes. The understanding gained of the factors that affect the relative isomers stabilities has allowed us to predict the stabilities of larger disubstituted carbon cages, for example, C₈₁Pt₂ heterofullerene.