  For the first time, we compute three-loop contributions to all triple
vertices in QCD at the symmetric point. The analytic results are obtained in
massless QCD with an arbitrary color group in the Landau gauge. All new loop
integrals are expressed in terms of harmonic polylogarithms at the sixth root
of unity. These corrections allow us to derive expressions for the four-loop
QCD beta function in a set of momentum-subtraction schemes.
