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The near-threshold 12C (0^+_2) resonance provides unique possibility for fasthelium burning in stars, as predicted by Hoyle to explain the observedabundance of elements in the Universe. Properties of this resonance arecalculated within the framework of the alpha-cluster model whose two-body andthree-body effective potentials are tuned to describe the alpha - alphascattering data, the energies of the 0^+_1 and 0^+_2 states, and the0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transitionradius are found in remarkable agreement with the experimental data. The0^+_2-state structure is described as a system of three alpha-particlesoscillating between the ground-state-like configuration and the elongated chainconfiguration whose probability exceeds 0.9.

Consistent alpha-cluster description of the 12C (0^+_2) resonance