text: Since the original discovery by Dan Shechtman, hundreds of quasicrystals have been reported and confirmed. Quasicrystals are found most often in aluminium alloys (Al–Li–Cu, Al–Mn–Si, Al–Ni–Co, Al–Pd–Mn, Al–Cu–Fe, Al–Cu–V, etc.), but numerous other compositions are also known (Cd–Yb, Ti–Zr–Ni, Zn–Mg–Ho, Zn–Mg–Sc, In–Ag–Yb, Pd–U–Si, etc.).
  Two types of quasicrystals are known. The first type, polygonal (dihedral) quasicrystals, have an axis of 8-, 10-, or 12-fold local symmetry (octagonal, decagonal, or dodecagonal quasicrystals, respectively). They are periodic along this axis and quasiperiodic in planes normal to it. The second type, icosahedral quasicrystals, are aperiodic in all directions. Icosahedral quasicrystals have a three dimensional quasiperiodic structure and possess fifteen 2-fold, ten 3-fold and six 5-fold axes in accordance with their icosahedral symmetry.
  Quasicrystals fall into three groups of different thermal stability:
  * Stable quasicrystals grown by slow cooling or casting with subsequent annealing,
  * Metastable quasicrystals prepared by melt spinning, and
  * Metastable quasicrystals formed by the crystallization of the amorphous phase.
  Except for the Al–Li–Cu system, all the stable quasicrystals are almost free of defects and disorder, as evidenced by X-ray and electron diffraction revealing peak widths as sharp as those of perfect crystals such as Si. Diffraction patterns exhibit fivefold, threefold, and twofold symmetries, and reflections are arranged quasiperiodically in three dimensions.
  The origin of the stabilization mechanism is different for the stable and metastable quasicrystals. Nevertheless, there is a common feature observed in most quasicrystal-forming liquid alloys or their undercooled liquids: a local icosahedral order. The icosahedral order is in equilibrium in the liquid state for the stable quasicrystals, whereas the icosahedral order prevails in the undercooled liquid state for the metastable quasicrystals.
  A nanoscale icosahedral phase was formed in Zr-, Cu- and Hf-based bulk metallic glasses alloyed with noble metals.
  Most quasicrystals have ceramic-like properties including high thermal and electrical resistance, hardness and brittleness, resistance to corrosion, and non-stick
  properties. Many metallic quasicrystalline substances are impractical for most applications due to their thermal instability; the Al–Cu–Fe ternary system and the Al–Cu–Fe–Cr and Al–Co–Fe–Cr quaternary systems, thermally stable up to 700 °C, are notable exceptions.
  The quasi-ordered droplet crystals could be formed under Dipolar forces in the Bose Einstein condensate. While the softcore Rydberg dressing interaction has forms triangular droplet-crystals, adding a Gaussian peak to the plateau type interaction would form multiple roton unstable points in the Bogoliubov spectrum. Therefore, the excitation around the roton instabilities would grow exponentially and form multiple allowed lattice constants leading to quasi-ordered periodic droplet crystals.