This article demonstrates the design potentials of a recently developed approach for generating smooth poly-hypar surfaces, freeform surfaces made of combinations of hyperbolic paraboloids (hypars). In a smooth poly-hypar surface, the double curvature of the individual hypar modules and the smooth connections between them ensure global bending-free structural behaviour. In this article, the structural analysis of a prestressed gridshell as a smooth poly-hypar surface is introduced. Graphic statics is used to evaluate and control the distribution of internal forces within the structure. Moreover, a case study, the Hypar Pavilion, is presented as a prestressed gridshell as a smooth poly-hypar surface structure. The Hypar Pavilion was prefabricated using lightweight materials and low-tech manufacturing techniques. The entire gridshell was manually built out of forty individual hypars, which were combined following a specific sequence to ensure the kinematic stability of the ongoing construction without scaffolding.