Triply periodic minimal surface structures and related geometries are widely identified in many natural systems, such as biological membranes and biophotonic structures in butterfly‐wing scales. Inspired by their marvelous and highly symmetrical structures and optimized physical properties, these structures have sparked immense interest for creating novel materials by extracting the design from nature. Significant progress has been made to understand these biological structures and fabricate artificial materials by top‐down and bottom‐up approaches for numerous applications in chemistry and materials science. Herein, research achievements, including theoretical and experimental discoveries, in both biological systems and the artificial synthesis of materials with triply periodic minimal surface structures and related materials are summarized. Recent developments in self‐assembled lyotropic liquid crystal phases, block copolymer systems, and their inorganic replicas are discussed in detail.

中文翻译：

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具有三重周期性最小表面和相关几何形状的材料概述：从生物结构到自组装系统

在许多自然系统中，广泛识别出三重周期性的最小表面结构和相关的几何形状，例如蝴蝶翼鳞片中的生物膜和生物光子结构。受到其奇妙而高度对称的结构和优化的物理特性的启发，这些结构激发了人们对通过从自然界中提取设计来创建新颖材料的浓厚兴趣。通过自上而下和自下而上的方法在化学和材料科学的众多应用中，了解这些生物结构和制造人造材料方面已取得了重大进展。在此，总结了在生物系统和具有三重周期性最小表面结构的材料的人工合成以及相关材料方面的研究成果，包括理论和实验发现。