The Faddeev equations in configuration space are used to study the ¹²C nucleus considered as the 3α cluster system. The model includes a phenomenological (Ali–Bodmer) pair potential having s, d and g partial wave components, a three-body potential and takes into account the Coulomb interaction. The range parameter of the three-body potential is fixed by adjusting the position of the diffraction minimum of the ¹²C elastic form factor. To choose this parameter, we apply an s-wave model that allows us to reproduce well observed characteristics of the 0⁺₁ and 0⁺₂ states. The model must be supplemented by the assumption of a distortion in the charge density of an α cluster inside the ¹²C nucleus. The calculations of the energies of several low-lying levels of ¹²C reveal unnaturally large contributions from the higher partial waves of the αα potential. We did not find the additional broad 0⁺ resonance which was recently reported (Kurokawa C and Kato K 2005 Phys. Rev. C 76 021301-1). The calculated resonance energies for the 0⁺₃ and 0⁺₄ states are in satisfactory agreement with the experimental data.