2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67732We give an example of a set $Ω\subset \R^5$ which is a finite union of unit cubes, such that $L^2(Ω)$ admits an orthonormal basis of exponentials $\{\frac{1}{|Ω|^{1/2}} e^{2πi ξ_j \cdot x}: ξ_j \in Λ\}$ for some discrete set $Λ\subset \R^5$, but which does not tile $\R^5$ by translations. This answers a conjecture of Fuglede in the negative, at least in 5 and higher dimensions.8 pages, no figures, 2 matrices; submitted, Math Research LettersCombinatoricsClassical Analysis and ODEs20K01; 42B99text