After the experimental evidence of polyynic as the stable form of cyclo[18]carbon, in the present paper, using ab initio electronic structure calculations, we show that this result is a symmetry breaking event, a consequence of the second-order Jahn-Teller effect. We show that the eigenfunctions associated with lowest unoccupied molecular orbitals (LUMO) and LUMO + 1, the excited states of this ring molecule, interact with the eigenfunctions associated with the ground state (occupied states), and this interaction stabilizes the less symmetric polyynic form of cyclo[18] carbon with D-9h symmetry, instead of the cumulenic form. The frontier state interactions are responsible for the distortions in the symmetry in the electronic structures, lowering the energy and making the polyynic form the stable one with alternating triple and single bonds.