In this paper, the possible ways of forming the midi-fullerene isomers, namely C22, C24 and C26, have been systematized. Three simplest mechanisms for their synthesizing are known. They are the fusion of carbon cupolas having the same symmetry; the fusion of fullerenes having compatible symmetry; embedding carbon dimers into initial fullerenes. The structures with minimal energy were formed through the use of the third mechanism retaining the topological three-fold symmetry. The symmetry order of studied fullerenes changed from the third to the sixth. The geometric modeling carried out in conjunction with the analysis of structures’ formation energies gives researchers a clear idea of the structure of the resulting fullerenes.