Structure of the 12j and 15j coefficients in the Bargmann approach

Generating functions of the 12j and 15j angular momentum recoupling coefficients are computed explicitly in the Bargmann formalism. Symmetry properties are deduced therefrom. A geometrical Möbius strip representation (originally due to Ord-Smith for the 12j case), which can be generalized to all n, suggests a 4n-fold symmetry for the 3nj coefficients (n ≥ 4).