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We describe the inclusive Racah matrices for the first non-(anti)symmetricrectangular representation R=[2,2] for quantum groups U_q(sl_N). Most of themhave sizes 2, 3, and 4 and are fully described by the eigenvalue hypothesis. Oftwo 6x6 matrices, one is also described in this way, but the other onecorresponds to the case of degenerate eigenvalues and is evaluated by thehighest weight method. Together with the much harder calculation for R=[3,1] inarXiv:1605.02313 and with the new method to extract exclusive matrices S and\bar S from the inclusive ones, this completes the story of Racah matrices for|R|\leq 4 and allows one to calculate and investigate the corresponding coloredHOMFLY polynomials for arbitrary 3-strand and arborescent knots.

Quantum Racah matrices and 3-strand braids in irreps R with |R|=4