DOI: 10.7764/RDLC.17.2.215Current architecture is characterized by specifying new typologies but not experienced until now in the engineering and architecture disciplines. Architectural free forms with non-euclidean geometries are being developed, which answer to logical analysis and parametric design, and which are tending to the mimesis of behaviour with the nature. Innovative research is developing advanced constructions of complex geometries and free forms by architects like Yushang Zhang, Rajiv Sewtahal, Riemer Postma and Qianqian Cai, Kahn, grupo Matsys, Acadia, AKT, Adler, Karan y Taylor, Emmanuel Ruffo… This paper addresses the analytical study of the set of technical solutions to the design of architectures based on geometric nature structures that will be applied to the building construction. Manufacturing and editing conditions of complex forms will characterize the innovative production systems of contemporary architecture. This study provides a strong documental foundation for research on the significance of new structural and constructive systems in the production of the current architecture.