Advances on triply periodic hyperbolic surface structures: from biological inspiration to artificial self-assembly

Triply periodic hyperbolic surfaces (TPHSs) are a class of complex structures that extend periodically throughout three-dimensional space and possess smooth surfaces with non-positive Gaussian curvature. They appear in a wide range of natural systems, from cellular membranes to butterfly wing scales and beetle exoskeletons. Owing to their unique geometries and extraordinary properties, TPHSs have attracted extensive attention and research interest. Detailed structural characterizations of naturally occurring TPHSs have been performed, and a variety of artificial analogs have been fabricated by top-down physical methods and bottom-up chemical approaches. These efforts have deepened our understanding of TPHSs and broadened their application scope. This review discusses the progress on TPHSs in biological systems and their artificial synthesis, and it surveys current applications of these structures in fields such as photonics, energy storage and conversion, catalysis, sensing, thermal management and mechanical metamaterials. It thereby provides a new framework linking biological structures to artificial structures. Finally, this review concludes by outlining current challenges and proposing directions for future research.