On a labeling for point group harmonics. II. Icosahedral group

The expressions for the Γ2, Γ5, Γ6, Γ8, and Γ9 representations are given in terms of those of Γ1 representations for neighboring angular momenta. The coefficients of the Γ4 representations are expressed in terms of those of Γ7 representations. Therefore, with an arbitrary choice of orthonormal sets of Γ1, Γ3, and Γ7 representations, orthonormal sets of other kinds of representations are well defined and can be labeled with the labels of parent representations. All Clebsch–Gordan coefficients are expressed in terms of those between parent representations (and a few others). Tables of all nondegenerate Γ1, Γ3, and Γ7 representations are given, for the axes of quantization of order 5. With some degenerate Γ3 and Γ7 representations, which are also given, any representation of integer or half‐integer angular momentum up to 27 can be obtained using some usual Clebsch–Gordan coefficients of SU(2).