  It was predicted qualitatively in ref.[1] that skyrmion matter at low density
is stable in an inhomogeneous phase where skyrmions condensate into lumps while
the remaining space is mostly empty. The aim of this paper is to proof
quantitatively this prediction. In order to construct an inhomogeneous medium
we distort the original FCC crystal to produce a phase of planar structures
made of skyrmions. We implement mathematically these planar structures by means
of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results
of our calculation of the average density and energy confirm the prediction
suggesting that the phase diagram of the dense skyrmion matter is a lot more
complex than a simple phase transition from the skyrmion FCC crystal lattice to
the half-skyrmion CC one. Our results show that skyrmion matter shares common
properties with standard nuclear matter developing a skin and leading to a
binding energy equation which resembles the Weiszaecker mass formula.
