  As an alternative approach to the infinite-array description of dense matter
in the Skyrme model, we report about the properties of a single skyrmion on a
compact 3-sphere of finite radius. The density of this matter can be increased
by decreasing the hypersphere radius. As in the array calculations one
encounters a transition to a distinct high density phase characterized by a
delocalization in energy and baryon charge and by increased symmetries. We will
argue that the high density phase has to be interpreted as chirally restored
one. The arguments are based on the formation of complete chiral multiplets and
the vanishing of the pionic massless Goldstone modes in the high-density
fluctuation spectrum. We show that the restoration of chiral symmetry is common
to any chirally invariant extension of the usual Skyrme model - whether via
higher-order contact terms or via the introduction of stabilizing vector mesons
which act over a finite range. (Talk at the workshop on ``Baryons as Skyrme
Solitons'', Siegen, Germany, Sept. 27-30, 1992)
