  Recently a formalism for a direct treatment of the Faddeev equation for the
three-nucleon bound state in three dimensions has been proposed. It relies on
an operator representation of the Faddeev component in the momentum space and
leads to a finite set of coupled equations for scalar functions which depend
only on three variables. In this paper we provide further elements of this
formalism and show the first numerical results for chiral NNLO nuclear forces.
