Multi‐Mechanical Regulation of 3D Printed Triply Periodic Hyperbolic Surfaces via Fourier Synthesis‐Based Free Modeling

Abstract Triply periodic hyperbolic surfaces (TPHSs) have attracted significant attention due to their exceptional lightweight and mechanical properties, which surpass those of other lattice structures. These advantages are primarily attributed to their unique periodic geometries and saddle‐shaped surface configurations. However, current structural design methods mainly rely on narrowband forward or multivariable inverse design strategies, which greatly limits the structural diversity and tunability of TPHSs, thereby hindering their further advancements in engineering applications. Herein, a hierarchical design method inspired by crystallographic Fourier synthesis is proposed, enabling the construction of arbitrary complex structures and the regulation of mechanical properties in multiple ways. By utilizing this approach, any structural types of TPHSs, including the most appealing primitive, gyroid, diamond‐like surfaces and their structural variants, are additively manufactured. This method enables precise manipulation of fine structural features to optimize 3D stress fields, significantly enhancing overall stiffness and strength. Moreover, this method facilitates the design of unbalanced TPHSs with rod‐like characteristics, enabling structural assembly through mortise‐tenon joints, which greatly expands the construction methodologies for such structures. This research substantially extends the design space of TPHS‐based structures and paves the way for their widespread application in advanced engineering contexts.