Three-photon Hong-Ou-Mandel interference at a multiport mixer

We consider a six-port triangular arrangement of beam splitters designed to couple three electromagnetic fields through U(3) unitary transformations. We present conditions for Hong-Ou-Mandel destructive interference of output triple coincidences when single photons are presented, one at each of the three input ports. Unlike the corresponding four-port effect, three-photon Hong-Ou-Mandel interference is sensitive to mixer phases and input-output port reversal.