Research on triply periodic minimal surfaces (TPMS) shows their high weight-saving potential for engineering applications. However, these studies include the manufacturing and material characteristics of the applied manufacturing process and are, therefore, difficult to compare. Comparisons with cellular solids widely used in aerospace engineering, such as Honeycombs, are unavailable. Therefore, this thesis investigates additively manufactured Gyroid, and Primitive sheet networks normalised with the characteristics of additively manufactured solid material to compare their relative modulus and relative strength with those of additively manufactured Honeycomb specimens. These relative mechanical characteristics are experimentally determined by testing additively manufactured solid and cellular specimens and simulating the infinite Gyroid compound in a finite element analysis. Based on the relative mechanical characteristics, different prediction models are compared, and a prediction model for TPMS sheet networks is selected. This chapter shows that the relative mechanical properties of Honeycombs under compressive loads outperform the relative mechanical properties of TPMS sheet networks. The finite element analysis shows the load-carrying potential of an infinite TPMS structure and reveals their independence of load direction and load type. However, this potential can only be approached with selective laser-sintered polyamide specimens, whereas stereolithography specimens show significantly lower compressive properties due to incomplete curing inside the structure. The mechanical prediction model derived from simulations and validated by experiments allows the preliminary design and failure prediction of larger structures of TPMS sheet networks, such as the core structure of additively manufactured suction panels. This enables the integration of TPMS suction panels into a wing sizing process.