Not yet reviewed by Pith; the record is open.

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.