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We show how a simple and elegant graphical notation can be used to derive theBiedenharn-Elliot identity for the 6j-symbol and we demonstrate how the sametechnique can be applied to obtain new identities for the 6j. We then employthe same method also in the context of 4D spin-foam gravity and propose ananalogous identity for the 15j-symbol.

Deriving identities for Wigner {nj}-symbols