Graduate Spin networks with different intertwiners

[Heidi]

Hi Pfs
Spin networks are defined by the way their links and their nodes are equipped with SU(2) representations and intertwiners.
Could you give an example of two different spin networks with the same number of nodes, links between them, the same coloring of the links (and their orientations) but have different intertwiners?
I would like to see how to assign squarable complex valued functions to them. how the intertwiners contract with the links.
thanks

 

[Heidi]

if i take the tensor product of two half integer SU(2) representation on 2 dimensional Hilbert space, i get a 4 dimensional matrix with
$1/2 \otimes 1/2 = 0 + 1$ and if i tensor it by it self i get the (0 + 1) + (1 + 0 + 1 + 2) representation with dimension 4 + 12 = 16. we see that 0 appears twice so there are two intertwiners. How do they act in the four valent node?
and what is the problem with the latex formula?