Racah algebra for the double trigonal group

A complete set of the 3jΓγ symbols for the double trigonal group [Formula: see text] is presented together with appropriate tables allowing evaluation of the numerical value of any Clebsch–Gordan coefficient for this group. The corresponding permutation matrices are derived. The complete set of 6Γ-symbols for both tensor and spinor representations is tabulated. The symmetry reduction problem for the chain [Formula: see text] involving a change of the axis of quantization is discussed in detail, and a full list of appropriate decomposition and reduction coefficients is given.