Tetragonal gyroid structure from symmetry manipulation: A brand-new member of the gyroid surface family

Gyroid (G) surfaces, the most famous naturally occurring triply periodic hyperbolic surfaces, are well known for their amazing properties closely associated with their intriguing symmetries. Although mathematicians and physicists are devoted to exploring new G surface family members, it remains a mystery whether any novel symmetrical G substructure can be experimentally validated beyond its well-known cubic-symmetrical systems. Herein, we report a tetragonal G substructure (shifted tG) obtained from a cooperative binary self-assembly system consisting of polystyrene- b -poly(acrylic acid) and cetyltrimethylammonium bromide. Shifted tG features periodic distributions of uneven matrix thicknesses with local concave free energies, exhibits an extraordinarily shifted double-gyroidal network with a low-symmetry space group of I 4 1 / a (no. 88), and possesses shifting-degree-dependent photonic band gaps that are never present in its unshifted cubic-symmetrical counterparts. The emergence of new G structures demonstrates a new frontier in the minimal surface subject, crucial for its exploration and innovation.