The aim of present work is to study electromagnetic properties of the ¹²C nucleus within the 3α cluster model. The αα-potentials of Ali-Bodmer and BFW are examined in describing the charge formfactor and root-mean square charge (RMS) radius of the carbon ground state. It was established that the l-independent Ali-Bodmer (AB) potential with a repulsive core yields a very strong underbinding with E = −0.60 MeV for the ground-state energy E_exp = −7.27 MeV. At the same time, the application of the deep BFW αα-potential with two Pauli forbidden states in the S-wave and a single forbidden state in the D-wave is associated with a complicated problem of removal of Pauli forbidden states from the 3α-functional space. A variational method on symmetrized Gaussian basis is employed. For the elimination of the 3α Pauli forbidden states we use the direct orthogonalization method. In the present work, we estimate the charge formfactor and RMS radius of the ¹²C nucleus within the 3α cluster model using the AB and BFW potential models. In order to reproduce the experimental energy value of the ¹²C nucleus ground state, we preliminarily add an attractive three-body potential (TBP) to the AB potential, while a repulsive TBP is employed for the BFW case.