The spatial structures have shown a great development through the years, mainly in the middle of the twentieth century in the post-war world, to become a constructive solution which gives lightness and stiffness, achieving longer spans and reducing energy and material consumptions. In Mexico City, the Sports Palace was completed in 1968 to become a landmark of Mexican architecture and an example of a low-cost lightweight dome. This paper shows the influences and geometric foundations of its design, development and typological transformations of the crossed arches, the final constructive solution of structural elements and the materials used in its construction, turning the material, the geometry as a structural typological solution, and the use of constructive and structural elements of previously used typologies into solutions to form new types, where Félix Candela uses the hyperbolic paraboloid employing new materials and applying geometry for the structural typological development of the shape of the Sports Palace achieving a dome which would become a typological model of international architecture.