Finite group theory for large systems. 2. Generating relations and irreducible representations for the icosahedral point group, I(h)

Generating relations and irreducible representations are given for the icosahedral point group, I(h), that are suited to computerized projection of symmetry-adapted bases of arbitrary spaces invariant to the group. With 120 elements I(h ) is a good prototype for symmetry-adaptation to a large finite nonabelian group. The four- and five-dimensional irreducible representations are obtained by coupling direct products of the three-dimensional irreducible representations using the symmetry-adaptation algorithm. The method is applied to the Hückel treatment of icosahedral C(20) fullerene.