The character of the energy spectrum of an icosahedral quasicrystal is
investigated in the tight-binding approximation. It is found that the
spectrum does not contain the hierarchical gap structure characterist
ic for a Canter set. Investigation of the smoothness of the energy spe
ctrum by the method of level statistics showed that the spectrum conta
ins a singular part. Suggestions are made concerning the form of the w
ave functions. (C) 1996 American Institute of Physics.