Spinor representation of icosahedral g orbitals

The four components of an icosahedral g orbital are represented by the irre ducible spinor representation (1/2 1/2) of SO1(3) x SO2(3) (or, equivalentl y, SO(4)), where the two SO(3) groups are associated with the irreducible r epresentations (IRs) T-1 and T-2 of the icosahedral group I. This enables t he properties of the icosahedral configurations g(N) to be calculated by th e familiar techniques of angular-momentum theory. The Coulomb interaction i s broken into three parts ei, two of which (e(0) and e(1)) are SO(4) scalar s, the third (e(2)) belonging to a combination of the various components M- 1 and M-2 of the IR (22) that form the scaler IR A of I. The similar matrix elements of e(2) for different N are explained by introducing the concepts of quasispin and complementarity that are analogous to those used in atomi c shell theory. Our angular-momentum basis is related to the icosahedral ba sis of Pooler with the aid of automorphisms of I that interchange T-1 and T -2. This is formalized through the introduction of the kaleidoscope operato r K, and the degeneracy of the T-1 and T-2 terms for all g(N) is expressed as a result of the invariance of the Coulomb interaction to the operations of the cyclic automorphism group C-4.