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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)

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