  This paper provides details of the massless three-loop three-point integrals
calculation at the symmetric point. Our work aimed to extend known two-loop
results for such integrals to the three-loop level. Obtained results can find
their application in regularization-invariant symmetric point
momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group
functions and various composite operator matrix elements. To calculate
integrals, we solve differential equations for auxiliary integrals by
transforming the system to the $\varepsilon$-form. Calculated integrals are
expressed through the basis of functions with uniform transcendental weight. We
provide expansion up to the transcendental weight six for the basis functions
in terms of harmonic polylogarithms with six-root of unity argument.
