j symbols and jm factors for all dihedral and cyclic groups

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Abstract
The methodology of earlier papers by Butler and Wybourne (1976) is used to obtain algebraic formulae for 6j symbols of the double dihedral and cyclic groups and the 3 jm factors for all possible imbeddings: Dm contains/implies Dn and Dm contains/implies Cn. The usual 3 jm symbols of angular momentum theory, that is for SO3 contains/implies SO2, do not have a phase choice which allows their factorisation into SO3 contains/implies Dinfinity and Dinfinity contains/implies SO2 3jm factors. The authors derive the change of phase necessary for factorisation, thus obtaining a relation between SO3 contains/implies Dinfinity factors and the SO3 contains/implies SO2 3jm symbols of standard angular momentum theory. The use of maximal imbeddings has removed the multiplicity problems encountered by other methods.