Five-Fold symmetry in materials science an example of emergence phenomenon*

In nature fivefold symmetry is oftent present .Flowers ,sea starts and seashell show five-fold symmetry. . Plants grow following the Fibonacci sequence which has the golden mean incorporated. Virus tends frequently packed as icosahedral symmetry. Also, artists since the Greek times to the modern era have used the golden mean. In all those cases the presence of fivefold symmetry can be easily  justified . In the case of solid state physics  in the 80’s crystals with fivefold symmetry were discovered (named quasicrystals). The discovery  produced a lot of questions.. In classical crystallography the fivefold rotational symmetry is forbidden, because rotations of 360/5 degrees do not reproduce the lattice. Nevertheless, fivefold structures are frequently observed. In this talk we discuss the physical reasons for these structures. We discuss quasicrystals as a complex system that emerges from the complex interaction of the enthalpy and the entropy.