There is a large literature on this subject. A popular article:
P.W. Stephens and A.I. Goldman The structue of quasicrystals Scientific American vol 264, April 1991, 24 - 31The most recent book:
Marjorie Senechal Quasicrystals and geometry Cambridge University Press 1996 Reviewed by C Radinand the original discovery of quasicrystals:
D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53 (1984), 1951-1953.