The chapter explains the studies the New Fundamentals Research Group is carrying out on the digital update of stereotomy. Between the various experiments, the chapter focuses on the group or prototypes designed by the geometry of the hyperbolic paraboloid, both at the macro (architectural organism) and micro scale (architectural elements). Several full-scale prototypes have been designed and built, using specific parametric codes, to define the geometrical morphogenesis properties of the built structural morphologies. Consequent theoretical reflections are fully explained