We perform a complete O(alpha4) calculation of the coupling of the Z b
oson to three photons via both fermion and W boson loops and keeping t
he full dependence on the quark and W masses. To evaluate the W boson
contribution to the fourth rank polarization tensor we use the unitary
gauge. We find that the contributions from fermion and boson loops ar
e remarkably similar. Expressions for the helicity amplitudes are pres
ented. The results are applied to the decay Z-->gammagammagamma where
we find a partial width of about 1.35 eV for m(top) > 91 GeV and sin2t
heta(W) = 0.23, of which the W boson loops account for approximately 0
.3 eV mainly through their interference with the fermion loops.