  The ground state of $^4$He confined in a system with the topology of a
cylinder can display properties of a solid, superfluid and liquid crystal. This
phase, which we call compactified supersolid (CSS), originates from wrapping
the basal planes of the bulk hcp solid into concentric cylindrical shells, with
several central shells exhibiting superfluidity along the axial direction. Its
main feature is the presence of a topological defect which can be viewed as a
disclination with Frank index $n=1$ observed in liquid crystals, and which, in
addition, has a superfluid core. The CSS as well as its transition to an
insulating compactified solid with a very wide hysteresis loop are found by ab
initio Monte Carlo simulations. A simple analytical model captures
qualitatively correctly the main property of the CSS -- a gradual decrease of
the superfluid response with increasing pressure.
