The high flux of the gas-phase beamline at the Elettra storage ring, Trieste (Italy), and the efficiency of a multicoincidence end station have been combined to measure the triple-differential cross section (TDCS) for the double photoionization (DPI) of He at excess energies E = 20 and 80 eV. The TDCS has been measured in the equal-energy-sharing kinematics, in which the kinetic energies of the two photoelectrons are equal (E1 = E2 = E/2). The experiments are compared with the predictions of a many-body Coulomb wave method and a convergent close-coupling calculation. The symmetrized gerade amplitudes of the He (DPI) extracted by the experiments as well as by the two calculations have been fitted by a Gaussian function. The results support the validity of the parametrization of the gerade amplitude via only one parameter, the full width at half maximum 1/2, of the Gaussian function, up to 80 eV above threshold.