  We obtain the lowest energy solutions for the skymion field equations and
their corresponding vortex structures. Two nondegenerate solutions emerge with
their vortex swirls in opposite directions. The solutions are associated with
an extremum property, which favors an array of almost hexagonal shape. We
predict that a regular hexagonal lattice must have a mix of skyrmions of both
swirls. Although our solutions could not keep the norm of the magnetization
constant at unity, their greatest deviation from unity occurred in regions
where the spins are far from planar; we show how to improve this situation.
