# Is a vortex crystal a supersolid?

Reading the article [Rev. Mod. Phys. 84, 759 (2012)] by Prokof'ev and Boninsegni, a supersolid is defined as a homogeneous phase of matter in which both density long-range order (i.e. ordered spatial modulation) and off-diagonal long-range order (i.e. superfluidity) exist simultaneously and appear spontaneously for the same species of particles.

Then several exotic examples are proposed, including solid $$^{4}\mathrm{He}$$ and dipolar quantum gases.

In my opinion, a more basic supersolid system should simply be a crystal of quantum vortices in a superfluid, since there is both superfluidity and spatial order.

This kind of state spontaneously emerge upon rotating a superfluid sample. Why is this broad and easily-accessible family of seemingly supersolid systems completely neglected? Am I missing something?