2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64307In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strata are locally modelled by $\R^k$ modulo the action of a discrete, possibly infinite, group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back. These spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting. We provide here the explicit construction of these spaces, and a thorough description of the stratification.LaTeX, 7 pagesSymplectic GeometryAlgebraic Geometry53D05; 53D20; 32S60; 52B20text