  In this paper, we construct Fourier quasicrystals with unit masses in
arbitrary dimensions. This generalizes a one-dimensional construction of
Kurasov and Sarnak. To do this, we employ a class of complex algebraic
varieties avoiding certain regions in $\mathbb{C}^n$, which generalize
hypersurfaces defined by Lee-Yang polynomials. We show that these are Delone
almost periodic sets that have at most finite intersection with every discrete
periodic set.
