The ground state of the molecule consisting of 10 carbon atoms in Cr-10(rg) "ring" conformation and the energy of its metastable C-10(st) "star" conformation are reported. The reaction coordinate for the isomeric transition C-10(st) -> C-10(rg) was calculated using density functional theory (DFT) with UB3LYP/6-31G(d,p). It was established that a 5-fold symmetry axis is conserved in this isomeric transition. The total energy of the ring isomer is by 10.33 eV (9.16 eV as zero-point energy corrected) lower than that of the star isomer. The energy barrier for the transition from the metastable star state to the ring state is 2.87 eV (3.57 eV as zero-point energy corrected). An analysis of possible chemical reactions in carbon plasma involving C-10(st), and C-10(rg), and leading to the formation of C-20 fullerenes was performed. It was revealed that the presence of the C-10(st), conformation in the reaction medium is a necessary condition for C20 fullerene formation. It was shown that the presence of hydrogen atoms in carbon plasma and UV radiation accelerate the C-10(st) -> C-10(rg) transition and thus suppress the C-20 fullerene formation.