  A measurement of the production of three isolated photons in proton-proton
collisions at a centre-of-mass energy $\sqrt{s}$ = 8 TeV is reported. The
results are based on an integrated luminosity of 20.2 fb$^{-1}$ collected with
the ATLAS detector at the LHC. The differential cross sections are measured as
functions of the transverse energy of each photon, the difference in azimuthal
angle and in pseudorapidity between pairs of photons, the invariant mass of
pairs of photons, and the invariant mass of the triphoton system. A measurement
of the inclusive fiducial cross section is also reported. Next-to-leading-order
perturbative QCD predictions are compared to the cross-section measurements.
The predictions underestimate the measurement of the inclusive fiducial cross
section and the differential measurements at low photon transverse energies and
invariant masses. They provide adequate descriptions of the measurements at
high values of the photon transverse energies, invariant mass of pairs of
photons, and invariant mass of the triphoton system.
