We have systematized possible ways of forming the isomers of midi-fullerenes, namely C30, C32, C34 C36, C38 and C40. Similar to the isomers of midi-fullerenes from C20 to C28, there are three the most natural mechanisms of their formation: 1) Embedding carbon dimers into initial fullerenes; 2) Fusion of carbon cupolas having the same symmetry; and 3) Fusion of fullerenes having compatible symmetry. The energies of the fullerenes calculated through the use of molecular mechanics are presented together with their graphs. It is found that in the majority of cases the minimum-energy fullerenes are those, having perfect and topological three-fold symmetries.