[Author] Titarenko, S. A. [Title] One can hear the shape of almost any drum! [AMS Subj-class] 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58J53 Isospectrality 35P25 Scattering theory for PDEs [Keywords] isospectral domains, isospectry mapping, disconnected subdomains [Abstract] A well-known problem of isospectral non-isometric domains is solved in this paper by constructing a new isospectry mapping. Investigating of its properties gives the main result: the domains of this kind are cellular ones. It follows from this in particular that convex and/or smooth isospectral drums are spectrally rigid, i.e. their shape can be "heard". [Comments] LaTeX, Russian, 11 pp. [Contact e-mail] titarenko.sa@gmail.com