those of the alloys discussed in this Letter, are metastable, and are produced by rapid cooling from the molten alloy. Later, stable quasicrystals were discovered. On the theoretical front the first treatment was in a Letter by Levine and Steinhardt , who had been researching generalizations of the Penrose tilings to three dimensions prior to the discovery of Shechtman et al. They showed that quasiperiodicity enables rotational symmetries forbidden to periodic crystals, first used the term quasicrystal in their Letter, and showed that their concepts accounted for the diffraction pattern observed by Shechtman et al. Subsequent theoretical developments by many researchers treated a quasicrystal as a projection of a higher dimensional crystal onto a three-dimensional space, or as an extension of the definition of a crystal in three-dimensional space. The influence of the Shechtman et al. discovery has been enormous, with publications, conferences and books on the subject still being produced, and showing no signs of abatement. When the Nobel Prize for the fractional quantum Hall effect experiment and the theory -- this Letter -- were announced, Robert Laughlin was interviewed by the New York Times. After seeing the experimental results he said that he formulated an explanation for the effect that was "completely wrong, and which, fortunately, was rejected by the referees at the journal [PRL] to which I submitted our paper". (Of course, papers are accepted or rejected by editors, not referees, but the reports are taken very seriously.) Soon he found a full explanation for the experimental