Tiles with no spectra in dimension 4 - Farkas, Bálint; Szilárd Gy., Révész (MATHEMATICA SCANDINAVICA, 2006)
We show by a counterexample that the "tiling $\Rightarrow$ spectral" part of Fuglede's Spectral Set Conjecture fails already in $\mathsf{Z}^4$ and $\mathsf {R}^4$.