A formula for (SU2) quantum 6j symbols exists. A formula expressing ordinary (q=1) 9j symbols in terms of 6j symbols is long known. Unfortunately, combining both (I tried it myself) got tricky - the associated graph K3,3 is nonplanar, at least one knot-type crossing is needed and first of all, this ruins the symmetry.

Can I find the quantum analogon of the standard sum over the product of three 6j symbols in the literature (or can someone post it here)?

allsuch choices. Perhaps the easiest (but perhaps to easy) way to do something like this would be to make all choices and compute an average. – Johannes Hahn Jun 11 '13 at 12:14