The two-dimensional unfolding of three-dimensional volumes allows architectural design and production methods to be rethought in a creative way. This paper reviews spatial and material properties of folded compositions in architecture, through a conceptual proposal based on professional and pedagogic experiences as well as new technologies for geometrical programming and digital fabrication, tested in five alternatives for one case study. The continuous and dynamic two-dimensional projection of a three-dimensional spatial situation provides a geometric relationship between the surface and volumetric configuration of a design, thus enabling a mathematical and operative connection between conditions of perception and production. The material expression of these configurations establishes a significant link between the conceptualisation of the design form, its geometric digital generation, its physical fabrication and overall appearance in a manner analogous to the design process used. The combination of folded compositions with the new technologies available further strengthens their potential, which embraces the fluid nature of human activity with continuous forms and delicately intricate geometries.