  We present next-to-leading order predictions for the production of triphoton
final states at the LHC and the Tevatron. Our results include the effect of
photon fragmentation for the first time and we are able to quantify the impact
of different isolation prescriptions. We find that calculations accounting for
fragmentation effects at leading order, and those employing a smooth cone
isolation where no fragmentation contribution is required, are in reasonable
agreement with one another. However, larger differences in the predicted rates
arise when higher order corrections to the fragmentation functions are
included. In addition we present full analytic results for the
$\gamma\gamma\gamma$ and $\gamma\gamma+$jet one-loop amplitudes. These
amplitudes, which are particularly compact, may be useful to future
higher-order calculations. Our results are available in the Monte Carlo code
MCFM.
