2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99910A `platycosm' is a flat Riemannian 3-manifold without boundary. In this paper we prove that there is (up to scale) a unique isospectral pair of compact platycosms.To appear in Math. Res. Lett. (2006). 20 pages, 20 figures. Minor changes to the 1st versionDifferential GeometrySpectral Theory58J53, 20H15text