Calculation of j and jm symbols for arbitrary compact groups. III. Application to SO3 ⊃ T ⊃ C3 ⊃ C1

The methodology developed in earlier papers is used to compute the 6j symbols and 3jm factors that arise in the group chain SO₃ ? T ? C₁. The relevant character theory is given and the 2j and 3j symbols calculated. Selection rules are used to predict which j symbols or jm factors are necessarily zero, and then a set of 6j fundamentals computed for T. The complete set of primitive 6j symbols are then computed by application of the orthogonality and Racah backcoupling relations. Primitive 3jm factors are calculated for SO₃ ? T and T ? C₃ and, from these, all the 3jm factors for T ? C₃ and some of those for SO₃ ? T computed. A complete table of non-equivalent 6j symbols for T and 3jm factors for T ? C₃ is given, together with a table for SO₃ ? T of all 3jm factors with j ≤ 2.