Icosahedral order in glass: Electronic properties

Icosahedral short-range order in glass is modeled by a crystalline packing of atoms in $S^3$, known as polytope 120. We diagonalize realistic electronic Hamiltonians using the symmetry group of polytope 120. We predict band structures for amorphous semiconductors and transition metals. Icosahedral order in silicon produces a gap in the center of the valence band. The absence of d-level splitting at the center of the Brillouin zone distinguishes icosahedrally ordered transition metals from their fcc counterparts. We use the d-band density of states of polytope 120 to understand band ferromagnetism in amorphous transition metals.