  The baby Skyrme model is studied with a novel choice of potential, $V=1/2
\phi_3^2$. This "easy plane" potential vanishes at the equator of the target
two-sphere. Hence, in contrast to previously studied cases, the boundary value
of the field breaks the residual SO(2) internal symmetry of the model.
Consequently, even the unit charge skyrmion has only discrete symmetry and
consists of a bound state of two half lumps. A model of long-range
inter-skyrmion forces is developed wherein a unit skyrmion is pictured as a
single scalar dipole inducing a massless scalar field tangential to the vacuum
manifold. This model has the interesting feature that the two-skyrmion
interaction energy depends only on the average orientation of the dipoles
relative to the line joining them. Its qualitative predictions are confirmed by
numerical simulations. Global energy minimizers of charges B=1,...,14,18,32 are
found numerically. Up to charge B=6, the minimizers have 2B half lumps
positioned at the vertices of a regular 2B-gon. For charges B >= 7, rectangular
or distorted rectangular arrays of 2B half lumps are preferred, as close to
square as possible.
