  We study static solutions of the standard Skyrme model with a pion mass.
Using approximately $10^5$ pseudo-random initial configurations made of single
Skyrmions in the non-symmetrized product Ansatz and an automatic detection of
repeated solutions, we find 409 local energy minimizers (Skyrmions) of the
model with baryon numbers 1 through 16, of which 383 are new. In particular, we
find new solutions for baryon numbers 5, 8, 9, 10, 11, 12, 13, 14, 15, and 16.
Our results for the number of solutions per baryon number suggest that this
number could grow either polynomially or exponentially. We identify new
families of solutions: sheets of Skyrmions in synchronized and antisynchronized
hexagonal layers (which we call graphene); chains of 2- and 3-tori; chain-like
solutions containing a hinge and many clustered Skyrmions. Contrary to common
lore, only the $B=12$ global energy minimizer is made of alpha particles or
some chunk of a cubic crystal, whereas the $B=9,11,14,15$ minimizers contain
the $B=7$ icosahedrally symmetric Skyrmion as a component. The $B=10,13,16$ are
symmetric graphene-like solutions. We find $B=5$ and $B=8$ minimizers with
numerically indistinguishable energies. The $B=8$ candidates are the chain of
two cubes, which is a chunk of the cubic Skyrme crystal and the fullerene-type
ball found originally by the rational map approximation. The $B=5$ global
minimizer is either the well-known $D_{2d}$ symmetric fullerene or a new
$C_{2v}$ symmetric solution. Finally, our findings show a large number of
solutions have no discrete symmetries or just one symmetry, contrary to the
common lore that Skyrmions are highly symmetric configurations.
