On intrinsic isometries to Euclidean space

It is a report on work in progress, joined with D. Burago and S. Ivanov. We consider compact length spaces which admit intrinsic isometries to Euclidean d-space. The class of these spaces is quite rich, it includes all d-dimensional Riemannian and sub-Riemannian manifolds, Euclidean polyhedra and more. The main result roughly states that the class of these spaces coincides with class of inverse limits of d-dimensional Euclidean polyhedra.