  Higher-order vertices at zero external momenta for the scalar field theory
describing the critical behaviour of the Ising model are studied within the
field-theoretical renormalization group (RG) approach in three dimensions.
Dimensionless six-point g_6 and eight-point g_8 effective coupling constants
are calculated in the three-loop approximation. Their numerical values,
universal at criticality, are estimated by means of the Pade and Pade-Borel
summation of the RG expansions found and by putting the renormalized quartic
coupling constant equal to its universal fixed-point value known from six-loop
RG calculations. The values of g_6^* obtained are compared with their analogs
resulting from the \epsilon-expansion, Monte Carlo simulations, the
Wegner--Houghton equations and the linked cluster expansion series. The
field-theoretical estimates for g_6^* are shown to be in a good agreement with
each other, differing considerably from the values given by other methods.
