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In part I of [1] we have developed the tensor and spin representation ofSO(4) in order to apply it to the simplicial decomposition of the Barrett-Cranemodel. We attach to each face of a triangle the spherical function constructedfrom the Dolginov-Biedenharn function.  In part II we apply the same technique to the Lorentz invariant state summodel. We need three new ingredients: the classification of the edges and thecorresponding subspaces that arises in the simplicial decomposition, the irrepsof SL(2,C) and its isomorphism to the bivectors appearing in the 4-simplices,the need of a zonal spherical function from the intertwining condition of thetensor product for the simple representations attached to the faces of thesimplicial decomposition.

Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model