  We present next-to-next-to-leading-order (NNLO) QCD corrections to the
production of three isolated photons in hadronic collisions at the fully
differential level. We employ qT subtraction within MATRIX and an efficient
implementation of analytic two-loop amplitudes in the leading-colour
approximation to achieve the first on-the-fly calculation for this process at
NNLO accuracy. Numerical results are presented for proton-proton collisions at
energies ranging from 7 TeV to 100 TeV. We find full agreement with the 8 TeV
results of arXiv:1911.00479 and confirm that NNLO corrections are indispensable
to describe ATLAS 8 TeV data. In addition, we demonstrate the significance of
NNLO corrections for future precision studies of triphoton production at higher
collision energies.
