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We present the first halo model based description of the Cosmic InfraredBackground (CIB) non-Gaussianity (NG) that is fully parametric. To this end, weintroduce, for the first time, a diagrammatic method to compute high orderpolyspectra of the 3D galaxy density field. It allows an easy derivation andvisualisation of the different terms of the polyspectrum. We apply thisframework to the power spectrum and bispectrum, and we show how to project themon the celestial sphere in the purpose of the application to the CIB angularanisotropies. Furthermore, we show how to take into account the particular caseof the shot noise terms in that framework. Eventually, we compute the CIBangular bispectrum at 857 GHz and study its scale and configurationdependencies, as well as its variations with the halo occupation distributionparameters. Compared to a previously proposed empirical prescription, suchphysically motivated model is required to describe fully the CIB anisotropiesbispectrum. Finally, we compare the CIB bispectrum with the bispectra of othersignals potentially present at microwave frequencies, which hints thatdetection of CIB NG should be possible above 220 GHz.

Non-Gaussianity of the Cosmic Infrared Background anisotropies I : Diagrammatic formalism and application to the angular bispectrum