and Gordon (1975a,b), who also presented stable algorithms for evaluating the $6j$-symbol numerically. A proof of a different sort was later given by Biedenharn and Louck (1981), based on showing that the Ponzano-Regge formula satisfies a set of defining properties of the $6j$-symbol.

More recently there have appeared more geometrical treatments of the asymptotics of the $6j$-symbol, that is, those based on geometric quantization (Kirillov 1976, Guillemin and Sternberg 1977, Woodhouse 1991), symplectic geometry and symplectic and Poisson reduction (Abraham and Marsden 1978, Arnold 1989, Marsden and Ratiu 1999) and other techniques. Among these are the works by Roberts (1999) and by Charles (2008). In addition, the $6j$-symbol has been taken as a test case for asymptotic studies of amplitudes that occur in quantum gravity (Barrett and Steele 2003, Freidel and Louapre 2003), in which the authors developed integral representations for the $6j$-symbol as integrals over products of the group manifold. There have also been quite a few other studies of asymptotics of particular spin networks, including Barrett and Williams (1999), Baez (2002), Rovelli and Speziale (2006), Hackett and Speziale (2007), Conrady and Freidel (2008), Alesci (2008), Barrett (2009), among others. We also mention the works of Gurau (2008), which 