is closely related to the K4 crystal (Laves' graph of girth ten). Applications In nature, self-assembled gyroid structures are found in certain surfactant or lipid mesophases and block copolymers. In a typical A-B diblock copolymer phase diagram, the gyroid phase can be formed at intermediate volume fractions between the lamellar and cylindrical phases. In A-B-C block copolymers, the double and alternating-gyroid phases can be formed. Such self-assembled polymer structures have found applications in experimental supercapacitors, solar cells photocatalysts, and nanoporous membranes. Gyroid membrane structures are occasionally found inside cells. Gyroid structures have photonic band gaps that make them potential photonic crystals. Single gyroid photonic crystals have been observed in biological structural coloration such as butterfly wing scales and bird feathers, inspiring work on biomimetic materials. The gyroid mitochondrial membranes found in the retinal cone cells of certain tree shrew species present a unique structure which may have an optical function. In 2017, MIT researchers studied the possibility of using the gyroid shape to turn bi-dimensional materials, such as graphene, into a three-dimensional structural material with low density, yet high tensile strength. Researchers from Cambridge University have shown the controlled chemical vapor deposition of sub–60 nm graphene gyroids. These interwoven structures are one of the smallest free-standing graphene 3D structures. They are conductive, mechanically stable, and easily transferable, and are of interest for a wide range of applications. The gyroid pattern has also found use in 3D printing for lightweight internal structures, due to its high strength, combined with speed and ease of printing using an FDM 3D printer. In an in silico study, researchers from the university hospital Charité in Berlin investigated the potential of gyroid architecture when used as a scaffold in a large bone defect in a rat femur. When comparing the regenerated bone within a gyroid scaffold compared to a traditional strut-like scaffold, they found that gyroid scaffolds led to less bone formation and attributed this reduced bone formation to the gyroid architecture hindering cell penetration. References External links Triply Periodic Minimal Surfaces at schoengeometry.com Gyroid at MathWorld Rotatable picture of a gyroid's period The gyroid at loomington's Virtual Minimal Surface Museum Electrochemical Nanofabrication: Principles and Applications Minimal surfaces