In the forties of the last century, Snyder introduced a quantized (deformed) relativistic model in the momentum space with de Sitter geometry. The authors in the present paper discuss an interesting duality between the Snyder model and de Sitter special relativity in coordinate space. Scales present in the geometries of both spaces: one is of the Planck length \(l_P\) order; the other proportional to the square root of the inverse of the cosmological constant \(R\sim\sqrt{\frac{3}{\Lambda}}\) are combined into the dimensionless constant \(l_PR^{-1}\sim10^{-61}\). In analogy to the gauge theory of gravity based on the Poincaré group, the authors propose the gauge-like approach departuring from the “localized” de Sitter group using a model of de Sitter gravity in the Lorentz gauge on an umbilical manifold.