## Nanocluster shape averaging with icosahedral symmetry

At lower temperature, the surface atoms of nanocluster only fluctuate around
their bounding positions, thus the surface shape of nanocluster remains
static. At higher temperature, not only the surface atoms travel across the
surface and between layers, but also the whole surface shape fluctuates a lot.
However, the fluctuation is around a equilibrium shape at the given
temperature. The concept has been described on
this page.
On the above page, the spherical shell is divided into cells unevenly by
solid angle. A better method is to divide the spherical shell evenly by the
points with icosahedral symmetry, whose coordinates are given by
the tables developed by R. H. Hardin, N. J. A. Sloane and W. D. Smith.
Best covering coordinates have been used here.

C++ implementation:
ihsurf.C with the support of
vector.h. Also given is an example xyz file
with 1212 points on the spherical surface. One results for the gold
icosahedral nanocluster with 5082 atoms (central atom missing) has been
given by this page.

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