  The density of states of the ideal three-dimensional Penrose tiling, a
quasicrystalline model, is calculated with a resolution of 10 meV. It is not
spiky. This falsifies theoretical predictions so far, that spikes of width
10-20 meV are generic for the density of states of quasicrystals, and it
confirms recent experimental findings. The qualitative difference between our
results and previous calculations is partly explained by the small number of k
points that has usually been included in the evaluation of the density of
states of periodic approximants of quasicrystals. It is also shown that both
the density of states of a small approximant of the three-dimensional Penrose
tiling and the density of states of the ideal two-dimensional Penrose tiling do
have spiky features, which also partly explains earlier predictions.
