  A superfluid having atomic scale superflow of a hexagonal lattice of vortex
and antivortex filaments, described by a single macroscopic wave function is
presented as a supersolid. As superfluid \he4 is pressurized, at a first order
transition, rotons (atomic scale current circulation, a vortex loop) not only
condense but also {\em expand and fuse into hexagonal or other complex
superflow patterns}. The vortex core contains an excess density of
non-condensate atoms. Further, a Kelvin (m = 0, necklace) mode condenses in the
vortex filaments. It results in a 3D atom density wave of hcp symmetry. In our
theory, superfluid phase stiffness, rather than atom localization, imitates a
solid like rigidity.
