  I discuss the use of spinors in the construction of spin-foam models, in
particular the form of the closure and simplicity constraints for triangles
that are space-like, i.e. with (area)$^2=\half S^{IJ}S_{IJ}>0$, regardless of
whether they belong the tetrahedra with a space-like or time-like normal,
emphasizing the role of the light-like 4-vector $u_t\sigma^I\bar u_t$. In the
quantization of the model, with the representations of SL(2,$\mathbb{C}$)
acting on spaces of functions of light-like vectors, one may use the canonical
basis of SU(2) representations, or the pseudobasis limited to the discrete
representations of SU(1,1); in alternative it is proposed to use instead a
basis of eigenstates of $(L_3,K_3)$, which might give matrix elements and
vertex functions with the same classical limit. A detailed example of a small
triangulation is presented, which among other things indicates, on the basis of
a classical calculation, that it would be impractical to limit oneself to
tetrahedra with time-like normals.
