  We apply two very different approaches to calculate Skyrmions with baryon
number B less than 23. The first employs the rational map ansatz, where
approximate charge B Skyrmions are constructed from a degree B rational map
between Riemann spheres. We use a simulated annealing algorithm to search for
the minimal energy rational map of a given degree B. The second involves the
numerical solution of the full non-linear time dependent equations of motion,
with initial conditions consisting of a number of well separated Skyrmion
clusters. In general, we find a good agreement between the two approaches. For
B greater than 6 almost all the solutions are of fullerene type, that is, the
baryon density isosurface consists of twelve pentagons and 2B-14 hexagons
arranged in a trivalent polyhedron. There are exceptional cases where this
structure is modified, which we discuss in detail. We find that for a given
value of B there are often many Skyrmions, with different symmetries, whose
energies are very close to the minimal value, some of which we discuss. We
present rational maps which are good approximations to these Skyrmions and
accurately compute their energy by relaxation using the full non-linear
dynamics.
