Triply periodic minimal surfaces (TPMS) are studied in material sciences because they have a high stiffness to weight ratio and variable relative density. However, their use in the design of building components at large scales has not been fully explored. This is partly due to their complex nature and the resulting difficult integration into the design process. In this paper, we therefore briefly discuss the state of the art and mathematical approaches for generation of TPMS and propose a digital design process controlling the main parameters of surface type and relative density. Performing a preliminary mechanical analysis for the Gyroid, Schwarz D and Lidinoid surfaces, we compare these parameters’ influence on the stiffness to density ratio within a hollow thin-walled concrete slab under consideration of possible 3D-printing with concrete. While the classification of TPMS poses an open mathematical problem, they offer a huge repertoire of potential structures and a valuable design tool for lightweight carbon reinforced concrete structures.