REFERENCES
1. Han, L.; Che, S. An overview of materials with triply periodic minimal surfaces and related geometry: from biological structures to self-assembled systems. Adv. Mater. 2018, 30, e1705708.
2. Emmer, M. Architecture and mathematics: soap bubbles and soap films. In: Williams K, Ostwald MJ, editors. Architecture and mathematics from antiquity to the future. Cham: Springer International Publishing; 2015. pp. 449-58.
4. Neovius, E. R. Bestimmung zweier speciellen periodischen Minimalflächen, auf welchen unendlich viele gerade Linien und unendlich viele ebene geodätische Linien liegen; Frenckell: Helsingfors, 1883. (in German). https://resolver.sub.uni-goettingen.de/purl?PPN591417707.
5. Schoen, A. H. Infinite periodic minimal surfaces without self-intersections; NASA Technical Note NASA TN D-5541; National Aeronautics and Space Administration: Washington, D.C., 1970. https://ntrs.nasa.gov/citations/19700020472.
6. Xiang, L.; Li, Q.; Li, C.; Yang, Q.; Xu, F.; Mai, Y. Block copolymer self-assembly directed synthesis of porous materials with ordered bicontinuous structures and their potential applications. Adv. Mater. 2023, 35, e2207684.
7. Chen, K.; Deng, Y.; Hu, T.; et al. Bioinspired periodic mesoporous tin oxides enable steady nonequilibrium chemical sensing for enhanced gas discrimination. Proc. Natl. Acad. Sci. U. S. A. 2026, 123, e2531153123.
8. Sheng, Q.; Li, Q.; Xiang, L.; Huang, T.; Mai, Y.; Han, L. Double diamond structured bicontinuous mesoporous titania templated by a block copolymer for anode material of lithium-ion battery. Nano Res. 2021, 14, 992-7.
9. Mall, A. P.; Bhandarkar, V. V.; Mandaloi, G.; Tandon, P. An overview of design and development of biomimetic bone scaffolds using heterogeneous TPMS lattice structures. Arch. Comput. Methods Eng. 2025, 32, 2429-56.
10. Liao, Y.; Liu, Y.; Ren, L.; et al. Nature-inspired bicontinuous-topology 3D-printed TPMS solar interfacial evaporator. Chem. Eng. J. 2026, 536, 176094.
11. Xiang, L.; Tang, C.; Xu, Z.; Xu, F.; Li, C.; Mai, Y. Functional porous cubosomes: synthesis and applications in energy storage and conversion. Acc. Mater. Res. 2025, 6, 939-51.
12. Sheng, Q.; Mao, W.; Han, L.; Che, S. Fabrication of photonic bandgap materials by shifting double frameworks. Chemistry 2018, 24, 17389-96.
13. Li, C.; Li, Q.; Kaneti, Y. V.; Hou, D.; Yamauchi, Y.; Mai, Y. Self-assembly of block copolymers towards mesoporous materials for energy storage and conversion systems. Chem. Soc. Rev. 2020, 49, 4681-736.
14. Cui, C.; Deng, Y.; Han, L. Bicontinuous cubic phases in biological and artificial self-assembled systems. Sci. China Mater. 2020, 63, 686-702.
15. Thayer, R. C.; Patel, N. H. A meta-analysis of butterfly structural colors: their color range, distribution and biological production. J. Exp. Biol. 2023, 226, jeb245940.
16. Ban, M.; Kim, S.; Lee, J. Polymer cubosome-templated bicontinuous materials: design principles, synthesis, and energy-environmental applications. Mater. Today 2026, 97, 103338.
17. Ranjith, M.; Khandke, S. A.; Niha, R.; Ansari, S.; Tamilnila, S. Bicontinuous cubic phase lipid nanoparticles cubosomes: formulation, characterization, and therapeutic applications. J. Drug Deliv. Ther. 2026, 16, 173-81.
18. Bhatt, A. H.; Patel, H. P.; Patel, P. R.; et al. Cubosomes in non-oral drug delivery: advancing precision therapeutics from bench to bedside. Int. J. Pharm. 2025, 684, 126108.
19. Barriga, H. M. G.; Holme, M. N.; Stevens, M. M. Cubosomes: the next generation of smart lipid nanoparticles? Angew. Chem. Int. Ed. Engl. 2019, 58, 2958-78.
20. Seidel, R.; Handrich, K.; Albéric, M.; et al. Comparative structural analysis of stereom polymorphs in the sea urchin test. Faraday Discuss. 2025, 261, 340-58.
21. Yang, T.; Chen, H.; Jia, Z.; et al. A damage-tolerant, dual-scale, single-crystalline microlattice in the knobby starfish, Protoreaster nodosus. Science 2022, 375, 647-52.
22. Zhao, X.; Xiong, Y.; Wang, W.; Zhang, W.; Zhang, D. Achieving structural white inspired by quasiordered microstructures in Morpho theseus. NPG Asia Mater. 2023, 15, 463.
23. Kobayashi, Y.; Ohnuki, R.; Yoshioka, S. Discovery of I-WP minimal-surface-based photonic crystal in the scale of a longhorn beetle. J. R. Soc. Interface 2021, 18, 20210505.
24. Tang, Y.; Xue, Y. N.; Yang, S. G.; et al. Gyroid Labyrinth of supertwisted double helices in a liquid crystal polymer. Angew. Chem. Int. Ed. Engl. 2026, 65, e22314.
25. Chen, C.; Poppe, M.; Poppe, S.; Tschierske, C.; Liu, F. Liquid organic frameworks: a liquid crystalline 8-connected network with body-centered cubic symmetry. Angew. Chem. Int. Ed. Engl. 2020, 59, 20820-5.
26. Wang, C.; Cui, C.; Deng, Q.; et al. Construction of the single-diamond-structured titania scaffold-recreation of the holy grail photonic structure. Proc. Natl. Acad. Sci. U. S. A. 2024, 121, e2318072121.
27. Lee, H.; Kwon, S.; Min, J.; et al. Thermodynamically stable plumber’s nightmare structures in block copolymers. Science 2024, 383, 70-6.
28. Lee, G. H.; Choi, S.; Yang, H.; et al. Self-assembled hollow gyroids with bicontinuous mesostructures: a highly robust electrocatalyst fixation platform. Adv. Mater. 2025, 37, e2412525.
29. Cui, C.; Wei, G.; Saba, M.; Cao, Y.; Han, L. Deep learning-assisted Fourier analysis for high-efficiency structural design: a case study on three-dimensional photonic crystals enumeration. Small 2026, 22, e11158.
30. Zhang, Y.; Zhang, J.; Zhou, Z.; et al. Multi-mechanical regulation of 3D printed triply periodic hyperbolic surfaces via fourier synthesis-based free modeling. Adv. Sci. (Weinh). 2025, 12, e70028.
31. Schamberger, B.; Ziege, R.; Anselme, K.; et al. Curvature in biological systems: its quantification, emergence, and implications across the Scales. Adv. Mater. 2023, 35, e2206110.
32. Himmelmann, M.; Pedersen, M. C.; Klatt, M. A.; Schönhöfer, P. W. A.; Evans, M. E.; Schröder-Turk, G. E. Amorphous bicontinuous minimal surface models and the superior Gaussian curvature uniformity of diamond, primitive and gyroid surfaces. P. Roy. Soc. A-Math. Phy. 2026, 482, 20250275.
34. Huse, D. A.; Leibler, S. Phase behaviour of an ensemble of nonintersecting random fluid films. J. Phys. France 1988, 49, 605-21.
35. Grosse-Brauckmann, K. Triply periodic minimal and constant mean curvature surfaces. Interface Focus 2012, 2, 582-8.
37. Maldovan, M.; Urbas, A. M.; Yufa, N.; Carter, W. C.; Thomas, E. L. Photonic properties of bicontinuous cubic microphases. Phys. Rev. B 2002, 65.
38. Saba, M.; Wilts, B. D.; Hielscher, J.; Schröder-Turk, G. E. Absence of circular polarisation in reflections of butterfly wing scales with chiral gyroid structure. Mater. Today: Proc. 2014, 1, 193-208.
40. Saranathan, V.; Osuji, C. O.; Mochrie, S. G.; et al. Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 11676-81.
41. Mao, W.; Cao, X.; Sheng, Q.; Han, L.; Che, S. Silica scaffold with shifted “plumber’s nightmare” networks and their interconversion into diamond networks. Angew. Chem. Int. Ed. Engl. 2017, 56, 10670-5.
42. Li, H.; Liu, Y.; Cao, X.; Han, L.; Jiang, C.; Che, S. A shifted double-diamond titania scaffold. Angew. Chem. Int. Ed. Engl. 2017, 56, 806-11.
43. Han, L.; Xu, D.; Liu, Y.; et al. Synthesis and characterization of macroporous photonic structure that consists of azimuthally shifted double-diamond silica frameworks. Chem. Mater. 2014, 26, 7020-8.
44. Hsueh, H. Y.; Ho, R. M. Bicontinuous ceramics with high surface area from block copolymer templates. Langmuir 2012, 28, 8518-29.
45. Andersson, S.; Hyde, S. T.; Larsson, K.; Lidin, S. Minimal surfaces and structures: from inorganic and metal crystals to cell membranes and biopolymers. Chem. Rev. 1988, 88, 221-42.
46. Schröder-Turk, G. E.; Fogden, A.; Hyde, S. T. Bicontinuous geometries and molecular self-assembly: comparison of local curvature and global packing variations in genus-three cubic, tetragonal and rhombohedral surfaces. Eur. Phys. J. B. 2006, 54, 509-24.
47. Anderson, D. M.; Davis, H. T.; Scriven, L. E.; Nitsche, J. C. C. Periodic surfaces of prescribed mean curvature. In: Prigogine I, Rice SA, editors. Advances in chemical physics. Wiley; 1990. pp. 337-96.
48. Han, Y.; Zhang, D.; Chng, L. L.; et al. A tri-continuous mesoporous material with a silica pore wall following a hexagonal minimal surface. Nat. Chem. 2009, 1, 123-7.
49. Hyde, S.; Schröder, G. Novel surfactant mesostructural topologies: between lamellae and columnar (hexagonal) forms. Curr Opin Colloid In 2003, 8, 5-14.
50. Schwarz, U. S.; Gompper, G. Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature. J. Chem. Phys. 2000, 112, 3792-802.
51. Pappas, G. D.; Brandt, P. W. Mitochondria. I. fine structure of the complex patterns in the mitochondria of Pelomyxa carolinensis Wilson (Chaos chaos L.). J. Biophys. Cytol. 1959, 6, 85-90.
52. Borysko, E.; Roslansky, J. Methods for correlated optical and electron microscopic studies of amoebae*. Ann. N. Y. Acad. Sci. 1959, 78, 432-47.
53. Daniels, E. W.; Breyer, E. P. Starvation effects on the ultrastructure of amoeba mitochondria. Z. Zellforsch. Mikrosk. Anat. 1968, 91, 159-69.
54. Deng, Y.; Marko, M.; Buttle, K. F.; Leith, A.; Mieczkowski, M.; Mannella, C. A. Cubic membrane structure in amoeba (Chaos carolinensis) mitochondria determined by electron microscopic tomography. J. Struct. Biol. 1999, 127, 231-9.
55. Deng, Y.; Mieczkowski, M. Three-dimensional periodic cubic membrane structure in the mitochondria of amoebae Chaos carolinensis. Protoplasma 1998, 203, 16-25.
56. Almsherqi, Z.; Margadant, F.; Deng, Y. A look through ‘lens’ cubic mitochondria. Interface Focus 2012, 2, 539-45.
57. Bykowski, M.; Mazur, R.; Buszewicz, D.; Szach, J.; Mostowska, A.; Kowalewska, Ł. Spatial nano-morphology of the prolamellar body in etiolated Arabidopsis thaliana plants with disturbed pigment and polyprenol composition. Front. Cell Dev. Biol. 2020, 8, 586628.
58. Hain, T. M.; Bykowski, M.; Saba, M.; Evans, M. E.; Schröder-Turk, G. E.; Kowalewska, Ł. SPIRE-a software tool for bicontinuous phase recognition: application for plastid cubic membranes. Plant Physiol. 2022, 188, 81-96.
59. Michielsen, K.; De Raedt, H.; Stavenga, D. G. Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi. J. R. Soc. Interface 2010, 7, 765-71.
60. Michielsen, K.; Stavenga, D. G. Gyroid cuticular structures in butterfly wing scales: biological photonic crystals. J. R. Soc. Interface 2008, 5, 85-94.
61. Argyros, A.; Manos, S.; Large, M. C.; McKenzie, D. R.; Cox, G. C.; Dwarte, D. M. Electron tomography and computer visualisation of a three-dimensional ‘photonic’ crystal in a butterfly wing-scale. Micron 2002, 33, 483-7.
62. Prum, R. O.; Quinn, T.; Torres, R. H. Anatomically diverse butterfly scales all produce structural colours by coherent scattering. J. Exp. Biol. 2006, 209, 748-65.
63. Schröder-Turk, G. E.; Wickham, S.; Averdunk, H.; et al. The chiral structure of porous chitin within the wing-scales of Callophrys rubi. J. Struct. Biol. 2011, 174, 290-5.
64. Winter, B.; Butz, B.; Dieker, C.; Schröder-Turk, G. E.; Mecke, K.; Spiecker, E. Coexistence of both gyroid chiralities in individual butterfly wing scales of Callophrys rubi. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 12911-6.
65. Inoue, M.; Saito, K.; Aoyama, H.; Inoue, H.; Ohnuki, R.; Yoshioka, S. Study on the chirality of gyroid photonic crystals in butterfly wing scales. Sci. Rep. 2025, 15, 20968.
66. Wilts, B. D.; Apeleo Zubiri, B.; Klatt, M. A.; et al. Butterfly gyroid nanostructures as a time-frozen glimpse of intracellular membrane development. Sci. Adv. 2017, 3, e1603119.
67. Jessop, A. L.; Clode, P. L.; Saunders, M.; et al. Hierarchical woven fibrillar structures in developing single gyroids in butterflies. Proc. Natl. Acad. Sci. U. S. A. 2025, 122, e2507297122.
68. Corkery, R. W.; Tyrode, E. C. On the colour of wing scales in butterflies: iridescence and preferred orientation of single gyroid photonic crystals. Interface Focus 2017, 7, 20160154.
69. Jessop, A. L.; Pirih, P.; Wang, L.; et al. Elucidating nanostructural organization and photonic properties of butterfly wing scales using hyperspectral microscopy. J. R. Soc. Interface 2024, 21, 20240185.
70. Galusha, J. W.; Richey, L. R.; Gardner, J. S.; Cha, J. N.; Bartl, M. H. Discovery of a diamond-based photonic crystal structure in beetle scales. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2008, 77, 050904.
71. Wilts, B. D.; Michielsen, K.; Kuipers, J.; De, Raedt. H.; Stavenga, D. G. Brilliant camouflage: photonic crystals in the diamond weevil, Entimus imperialis. Proc. Biol. Sci. 2012, 279, 2524-30.
72. Wu, X.; Erbe, A.; Raabe, D.; Fabritius, H. Extreme optical properties tuned through phase substitution in a structurally optimized biological photonic polycrystal. Adv. Funct. Mater. 2013, 23, 3615-20.
73. Saranathan, V.; Seago, A. E.; Sandy, A.; et al. Structural diversity of arthropod biophotonic nanostructures spans amphiphilic phase-space. Nano Lett. 2015, 15, 3735-42.
74. Parisotto, A.; Steiner, U.; Cabras, A. A.; Van Dam, M. H.; Wilts, B. D. Pachyrhynchus weevils use 3D photonic crystals with varying degrees of order to create diverse and brilliant displays. Small 2022, 18, e2200592.
75. Edagawa, K.; Kanoko, S.; Notomi, M. Photonic amorphous diamond structure with a 3D photonic band gap. Phys. Rev. Lett. 2008, 100, 013901.
76. Djeghdi, K.; Steiner, U.; Wilts, B. D. 3D Tomographic analysis of the order-disorder interplay in the Pachyrhynchus congestus mirabilis weevil. Adv. Sci. (Weinh). 2022, 9, e2202145.
77. Bauernfeind, V.; Saranathan, V.; Djeghdi, K.; et al. Not only a matter of disorder in I-WP minimal surface-based photonic networks: diffusive structural color in Sternotomis amabilis longhorn beetles. Mater. Today Adv. 2024, 23, 100524.
78. Bauernfeind, V.; Djeghdi, K.; Gunkel, I.; Steiner, U.; Wilts, B. D. Photonic amorphous I-WP-like networks create angle-independent colors in Sternotomis virescens Longhorn beetles. Adv. Funct. Mater. 2024, 34, 2302720.
79. Saranathan, V.; Narayanan, S.; Sandy, A.; Dufresne, E. R.; Prum, R. O. Evolution of single gyroid photonic crystals in bird feathers. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2101357118.
80. Donnay, G.; Pawson, D. L. X-ray diffraction studies of echinoderm plates. Science 1969, 166, 1147-50.
82. Jessop, A. L.; Millsteed, A. J.; Kirkensgaard, J. J. K.; Shaw, J.; Clode, P. L.; Schröder-Turk, G. E. Composite material in the sea urchin Cidaris rugosa: ordered and disordered micrometre-scale bicontinuous geometries. J. R. Soc. Interface 2024, 21, 20230597.
83. Nissen, H. U. Crystal orientation and plate structure in echinoid skeletal units. Science 1969, 166, 1150-2.
84. Gorzelak, P.; Kołbuk, D.; Stolarski, J.; et al. A Devonian crinoid with a diamond microlattice. Proc. Biol. Sci. 2023, 290, 20230092.
85. Guo, X.; Li, X.; Wang, E.; Fuh, J. Y.; Lu, W. F.; Zhai, W. Bioinspired hierarchical diamond triply periodic minimal surface lattices with high energy absorption and damage tolerance. Addit. Manuf. 2023, 76, 103792.
86. Wang, H. F.; Chiu, P. T.; Yang, C. Y.; et al. Networks with controlled chirality via self-assembly of chiral triblock terpolymers. Sci. Adv. 2020, 6, eabc3644.
87. Yang, K. C.; Reddy, A.; Tsai, H. W.; Zhao, W.; Grason, G. M.; Ho, R. M. Breaking mirror symmetry of double gyroids via self-assembly of chiral block copolymers. ACS Macro Lett. 2022, 11, 930-4.
88. Hou, L.; Xu, Z.; Dong, Q.; Shi, A.; Li, W. Stabilizing DG, DD, and DP Bicontinuous network phases in pure AB-type block copolymers beyond relieving packing frustration. Macromolecules 2024, 57, 2165-75.
89. Xie, Q.; Qiang, Y.; Li, W. Single gyroid self-assembled by linear BABAB pentablock copolymer. ACS Macro Lett. 2022, 11, 205-9.
90. Cheng, Y.; Xu, Z.; Li, W. Understand the relative stability of single-gyroid to double-gyroid in AB-type block copolymer: chain packing and geometric analysis. Macromolecules 2024, 57, 9167-80.
91. La, Y.; Park, C.; Shin, T. J.; Joo, S. H.; Kang, S.; Kim, K. T. Colloidal inverse bicontinuous cubic membranes of block copolymers with tunable surface functional groups. Nat. Chem. 2014, 6, 534-41.
92. Ha, S.; La, Y.; Kim, K. T. Polymer cubosomes: infinite cubic mazes and possibilities. Acc. Chem. Res. 2020, 53, 620-31.
93. Park, S. J.; Bates, F. S.; Dorfman, K. D. Single gyroid in H-shaped block copolymers. Phys. Rev. Mater. 2023, 7.
94. Cho, A.; La, Y.; Jeoung, S.; et al. Mix-and-match assembly of block copolymer blends in solution. Macromolecules 2017, 50, 3234-43.
95. Chu, C.; Pei, R.; Chen, H. Order-order transition from ordered bicontinuous double diamond to hexagonally packed cylinders in stereoregular diblock copolymer/homopolymer blends. Macromolecules 2018, 51, 8493-500.
96. Takagi, H.; Yamamoto, K.; Okamoto, S. Ordered-bicontinuous-double-diamond structure in block copolymer/homopolymer blends. EPL 2015, 110, 48003.
97. Takagi, W.; Suzuki, J.; Aoyama, Y.; Mihira, T.; Takano, A.; Matsushita, Y. Bicontinuous double-diamond structures formed in ternary blends of ab diblock copolymers with block chains of different lengths. Macromolecules 2019, 52, 6633-40.
98. Takagi, H.; Yamamoto, K. Effect of block copolymer composition and homopolymer molecular weight on ordered bicontinuous double-diamond structures in binary blends of polystyrene-polyisoprene block copolymer and polyisoprene homopolymer. Macromolecules 2021, 54, 5136-43.
99. Wang, X.; Feng, Y.; Lu, S.; Feng, X.; Wang, G.; Li, W. SCFT-guided experimental fabrication of double-diamond structures in A1B/A2B block copolymer binary blends. Macromolecules 2025, 58, 9776-85.
100. Duan, C.; Wang, Z. G. End-functionalized ions promote stability of highly frustrated phases in diblock copolymers. Proc. Natl. Acad. Sci. U. S. A. 2026, 123, e2621115123.
101. Hendeniya, N.; Chittick, C.; Hillery, K.; Abtahi, S.; Mosher, C.; Chang, B. Revealing the kinetic phase behavior of block copolymer complexes using solvent vapor absorption-desorption isotherms. ACS Appl. Mater. Interfaces 2024, 16, 18144-53.
102. Lin, Z.; Liu, S.; Mao, W.; et al. Tunable self-assembly of diblock copolymers into colloidal particles with triply periodic minimal surfaces. Angew. Chem. Int. Ed. Engl. 2017, 56, 7135-40.
103. Dolan, J. A.; Korzeb, K.; Dehmel, R.; et al. Controlling self-assembly in gyroid terpolymer films by solvent vapor annealing. Small 2018, 14, e1802401.
104. Chang, C.; Chen, Y.; Ho, R. Metastable network phases from controlled self-assembly of high- χ block copolymers. Phys. Rev. Mater. 2024, 8, 030301.
105. Yeh, S. L.; Chang, C. Y.; Ho, R. M. Reticulation of block copolymer nanostructures from perforation. ACS Appl. Mater. Interfaces 2025, 17, 12676-85.
106. Jacobs, A. G.; Liedel, C.; Peng, H.; et al. Kinetics of block copolymer phase segregation during sub-millisecond transient thermal annealing. Macromolecules 2016, 49, 6462-70.
107. Luan, J.; Wang, D.; Kok, N. P.; Moslehi, N.; Voets, I. K.; Wilson, D. A. Dynamic pathways in energy landscapes guiding supramolecular Janus dendrimer self-assemblies between lamellar and cubic architectures. Nat. Commun. 2025, 16, 8075.
108. Deng, Q.; Liu, Y.; Cao, Y.; Han, L. Formation of a silica scaffold with a hyperbolic surface structure as a time-frozen glimpse by ultraviolet curing. Interface Focus 2026, 16, 20250091.
109. Feng, J.; Fu, J.; Yao, X.; He, Y. Triply periodic minimal surface (TPMS) porous structures: from multi-scale design, precise additive manufacturing to multidisciplinary applications. Int. J. Extrem. Manuf. 2022, 4, 022001.
110. Koroľ, M.; Töröková, M.; Tkáč, J. Triply periodic minimal surface (TPMS) cellular structures: modeling, manufacturing, and application perspectives - a review. J. Compos. Sci. 2026, 10, 439.
111. Lee, H.; Lee, D. H.; Hyun, J.; et al. Development and prospects of zirconia 3D printing for artificial prosthesis applications. Chem. Rev. 2026, 126, 8203-33.
112. Pflaum, M.; Barbian, K. P.; Neuhaus, F.; et al. From fiber bundles to architected membranes: triply periodic minimal surface architectures for biohybrid artificial lungs. Adv. Mater. 2026, 38, e74361.
113. Wang, Y.; Lei, Y.; Cui, R.; et al. A genus-tuning design on minimal surfaces for open-cell mechanical metamaterials. Int. J. Mech. Sci. 2026, 313, 111304.
114. Nuhu, A. A.; Elmoghazy, Y. H.; Al Mahmoud, Z.; Petrů, J.; Sahmani, S.; Safaei, B. TPMS-based hyperboloidal primitive architectured structures with a novel hybridization method. Int. J. Mech. Sci. 2026, 312, 111206.
115. Daynes, S. Isotropic cellular structure design strategies based on triply periodic minimal surfaces. Addit. Manuf. 2024, 81, 104010.
116. Fu, J.; Ding, J.; Zhang, L.; Qu, S.; Song, X.; Fu, M. Development of conformal shell lattices via laser powder bed fusion and unraveling their mechanical responses via modeling and experiments. Addit. Manuf. 2023, 62, 103406.
117. Jin, Y.; Zou, S.; Pan, B.; Li, G.; Shao, L.; Du, J. Biomechanical properties of cylindrical and twisted triply periodic minimal surface scaffolds fabricated by laser powder bed fusion. Addit. Manuf. 2022, 56, 102899.
118. Perna, I.; Ferraro, R.; Coppola, S.; Caserta, S. Phase separation in block copolymer systems: From thermodynamics to industrial applications. Adv. Colloid Interface Sci. 2026, 352, 103841.
119. Hümöller, J. M.; Oviedo, O. A. Exploring liquid crystal properties through the two-phase thermodynamic model: structural, dynamic, and thermodynamic properties. J. Chem. Theory Comput. 2025, 21, 2219-34.
120. Meng, Z.; Wang, S.; Xu, G.; Qiu, S.; Xu, X. Recent advances: kinetically controlled chiral matters for soft assembly, motion and optoelectronics. Laser Photonics Rev. 2025, 19, 2401754.
121. Fielden, S. D. P. Kinetically controlled and nonequilibrium assembly of block copolymers in solution. J. Am. Chem. Soc. 2024, 146, 18781-96.
122. Xu, Z.; Dong, Q.; Li, W. Architectural design of block copolymers. Macromolecules 2024, 57, 1869-84.
123. Chen, P.; Mahanthappa, M. K.; Dorfman, K. D. Stability of cubic single network phases in diblock copolymer melts. J. Polym. Sci. 2022, 60, 2543-52.
124. Dimitriyev, M. S.; Reddy, A.; Grason, G. M. Medial packing, frustration, and competing network phases in strongly segregated block copolymers. Macromolecules 2023, 56, 7184-202.
125. Dimitriyev, M. S.; Greenvall, B. R.; Mathew, R.; Grason, G. M. Not even metastable: cubic double-diamond in diblock copolymer melts. ACS Macro Lett. 2025, 14, 1291-8.
126. Wang, L.; Urbas, A. M.; Li, Q. Nature-inspired emerging chiral liquid crystal nanostructures: from molecular self-assembly to DNA mesophase and nanocolloids. Adv. Mater. 2020, 32, e1801335.
127. Bisoyi, H. K.; Li, Q. Light-directing chiral liquid crystal nanostructures: from 1D to 3D. Acc. Chem. Res. 2014, 47, 3184-95.
128. Wang, Y.; Singh, G.; Agra-Kooijman, D. M.; et al. Room temperature heliconical twist-bend nematic liquid crystal. CrystEngComm 2015, 17, 2778-82.
129. Ma, L. L.; Li, C. Y.; Pan, J. T.; et al. Self-assembled liquid crystal architectures for soft matter photonics. Light Sci. Appl. 2022, 11, 270.
130. Prakash, J.; Chandran, A.; Biradar, A. M. Scientific developments of liquid crystal-based optical memory: a review. Rep. Prog. Phys. 2017, 80, 016601.
131. Govindan, I.; Paul, A.; Rama, A.; et al. Mesogenic architectures for advanced drug delivery: interrogating lyotropic and thermotropic liquid crystals. AAPS PharmSciTech. 2024, 26, 6.
132. Shan, X.; Luo, L.; Yu, Z.; You, J. Recent advances in versatile inverse lyotropic liquid crystals. J. Control. Release 2022, 348, 1-21.
133. Zhai, J.; Sarkar, S.; Tran, N.; Pandiancherri, S.; Greaves, T. L.; Drummond, C. J. Tuning nanostructured lyotropic liquid crystalline mesophases in lipid nanoparticles with protic ionic liquids. J. Phys. Chem. Lett. 2021, 12, 399-404.
134. Mezzenga, R.; Seddon, J. M.; Drummond, C. J.; Boyd, B. J.; Schröder-Turk, G. E.; Sagalowicz, L. Nature-inspired design and application of lipidic lyotropic liquid crystals. Adv. Mater. 2019, 31, e1900818.
135. Liang, B.; Cheng, Y.; Liu, X.; et al. Chiral liquid crystals based on pillararene and supramolecular self-assembly-induced chirality amplification. Sci. China Chem. 2024, 67, 3373-81.
136. Shimomura, Y.; Tokita, M.; Kawamura, A.; Watanabe, J.; Konishi, G. Fluorinated poly(pentylene 4,4′-bibenzoate)s with low isotropization temperatures and unique phase transition behavior. Macromolecules 2023, 56, 5152-61.
137. Che, A.; Zellmann-Parrotta, C. O.; Sarkar, D.; et al. Cyclodextrin-based liquid crystals: a novel approach to promote the formation of thermotropic cubic mesophases and their potential applications as electrolytes. Carbohydr. Polym. 2025, 359, 123587.
138. Cao, Y.; Tschierske, C.; Liu, F. Structural complexity, network formation and spontaneous chirality in soft-matter self-assembly. Acc. Chem. Res. 2026, 59, 1983-96.
139. Levelut, A.; Clerc, M. Structural investigations on ‘smectic D’ and related mesophases. Liq. Cryst. 1998, 24, 105-16.
140. Zeng, X.; Ungar, G.; Impéror-Clerc, M. A triple-network tricontinuous cubic liquid crystal. Nat. Mater. 2005, 4, 562-7.
141. Zeng, X.; Prehm, M.; Ungar, G.; Tschierske, C.; Liu, F. Formation of a double diamond cubic phase by thermotropic liquid crystalline self-assembly of bundled bolaamphiphiles. Angew. Chem. Int. Ed. Engl. 2016, 55, 8324-7.
142. Zeng, X.; Poppe, S.; Lehmann, A.; et al. A self-assembled bicontinuous cubic phase with a single-diamond network. Angew. Chem. Int. Ed. Engl. 2019, 58, 7375-9.
143. Poppe, S.; Cheng, X.; Chen, C.; et al. Liquid organic frameworks: the single-network “plumber’s nightmare” bicontinuous cubic liquid crystal. J. Am. Chem. Soc. 2020, 142, 3296-300.
144. Cao, Y.; Alaasar, M.; Zhang, L.; Zhu, C.; Tschierske, C.; Liu, F. Supramolecular meso-trick: ambidextrous mirror symmetry breaking in a liquid crystalline network with tetragonal symmetry. J. Am. Chem. Soc. 2022, 144, 6936-45.
145. Cai, X.; Hauche, S.; Poppe, S.; et al. Network phases with multiple-junction geometries at the gyroid-diamond transition. J. Am. Chem. Soc. 2023, 145, 1000-10.
146. Cao, Y.; Alaasar, M.; Nallapaneni, A.; et al. Molecular packing in double gyroid cubic phases revealed via resonant soft X-ray scattering. Phys. Rev. Lett. 2020, 125, 027801.
147. Poppe, S.; Chen, C.; Wagner, M.; Cao, Y.; Liu, F.; Tschierske, C. A series of three liquid crystalline cubic phases with an alternating sequence of single- and double-network structures. Chem. Commun. (Camb) 2025, 61, 18629-32.
149. Luzzati, V.; Tardieu, A.; Gulik-Krzywicki, T. Polymorphism of lipids. Nature 1968, 217, 1028-30.
150. Templer, R. H.; Seddon, J. M.; Warrender, N. A.; et al. Inverse bicontinuous cubic phases in 2:1 fatty acid/phosphatidylcholine mixtures. The effects of chain length, hydration, and temperature. J. Phys. Chem. B. 1998, 102, 7251-61.
151. Tang, T. Y.; Seddon, A. M.; Jeworrek, C.; et al. The effects of pressure and temperature on the energetics and pivotal surface in a monoacylglycerol/water gyroid inverse bicontinuous cubic phase. Soft Matter 2014, 10, 3009-15.
152. Vacklin, H.; Khoo, B. J.; Madan, K. H.; Seddon, J. M.; Templer, R. H. The bending elasticity of 1-monoolein upon relief of packing stress. Langmuir 2000, 16, 4741-8.
153. Tang, T. Y.; Brooks, N. J.; Jeworrek, C.; et al. Hydrostatic pressure effects on the lamellar to gyroid cubic phase transition of monolinolein at limited hydration. Langmuir 2012, 28, 13018-24.
154. Shearman, G. C.; Khoo, B. J.; Motherwell, M. L.; et al. Calculations of and evidence for chain packing stress in inverse lyotropic bicontinuous cubic phases. Langmuir 2007, 23, 7276-85.
155. Tyler, A. I.; Barriga, H. M.; Parsons, E. S.; et al. Electrostatic swelling of bicontinuous cubic lipid phases. Soft Matter 2015, 11, 3279-86.
156. Barriga, H. M.; Tyler, A. I.; McCarthy, N. L.; et al. Temperature and pressure tuneable swollen bicontinuous cubic phases approaching nature’s length scales. Soft Matter 2015, 11, 600-7.
157. Kulkarni, C. V.; Tang, T.; Seddon, A. M.; Seddon, J. M.; Ces, O.; Templer, R. H. Engineering bicontinuous cubic structures at the nanoscale - the role of chain splay. Soft Matter 2010, 6, 3191.
158. Tang, T. Y.; Brooks, N. J.; Ces, O.; Seddon, J. M.; Templer, R. H. Structural studies of the lamellar to bicontinuous gyroid cubic (
159. Tran, N.; Zhai, J.; Conn, C. E.; Mulet, X.; Waddington, L. J.; Drummond, C. J. Direct visualization of the structural transformation between the lyotropic liquid crystalline lamellar and bicontinuous cubic mesophase. J. Phys. Chem. Lett. 2018, 9, 3397-402.
160. Van ’t Hag, N.; Gras, S. L.; Conn, C. E.; Drummond, C. J. Lyotropic liquid crystal engineering moving beyond binary compositional space - ordered nanostructured amphiphile self-assembly materials by design. Chem. Soc. Rev. 2017, 46, 2705-31.
161. Gao, C.; Sakamoto, Y.; Sakamoto, K.; Terasaki, O.; Che, S. Synthesis and characterization of mesoporous silica AMS-10 with bicontinuous cubic Pn
162. Sorenson, G. P.; Schmitt, A. K.; Mahanthappa, M. K. Discovery of a tetracontinuous, aqueous lyotropic network phase with unusual 3D-hexagonal symmetry. Soft Matter 2014, 10, 8229-35.
163. Angelopoulou, P. P.; Moutsios, I.; Manesi, G.; Ivanov, D. A.; Sakellariou, G.; Avgeropoulos, A. Designing high χ copolymer materials for nanotechnology applications: a systematic bulk vs. thin films approach. Prog. Polym. Sci. 2022, 135, 101625.
164. Matsen, M. W.; Bates, F. S. Unifying weak- and strong-segregation block copolymer theories. Macromolecules 1996, 29, 1091-8.
165. Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 1980, 13, 1602-17.
166. Olvera de la Cruz, M. Theory of microphase separation in block copolymer solutions. J. Chem. Phys. 1989, 90, 1995-2002.
167. Bates, F. S.; Fredrickson, G. H. Block copolymer thermodynamics: theory and experiment. Annu. Rev. Phys. Chem. 1990, 41, 525-57.
168. Zhang, B.; Zheng, C.; Bates, F. S.; Lodge, T. P. Self-assembly of charged diblock copolymers with reduced backbone polarity. ACS Appl. Polym. Mater. 2023, 5, 2223-9.
169. Russell, S. T.; Bae, S.; Subramanian, A.; et al. Priming self-assembly pathways by stacking block copolymers. Nat. Commun. 2022, 13, 6947.
170. Bates, F. S.; Fredrickson, G. H. Block copolymers- designer soft materials. Phys. Today 1999, 52, 32-8.
171. Wong, C. K.; Qiang, X.; Müller, A. H.; Gröschel, A. H. Self-assembly of block copolymers into internally ordered microparticles. Prog. Polym. Sci. 2020, 102, 101211.
172. Khandpur, A. K.; Foerster, S.; Bates, F. S.; et al. Polyisoprene-polystyrene diblock copolymer phase diagram near the order-disorder transition. Macromolecules 1995, 28, 8796-806.
173. Matsen, M. W.; Schick, M. Stable and unstable phases of a diblock copolymer melt. Phys. Rev. Lett. 1994, 72, 2660-3.
174. Cochran, E. W.; Garcia-Cervera, C. J.; Fredrickson, G. H. Stability of the gyroid phase in diblock copolymers at strong segregation. Macromolecules 2006, 39, 2449-51.
175. Hajduk, D. A.; Harper, P. E.; Gruner, S. M.; et al. The gyroid: a new equilibrium morphology in weakly segregated diblock copolymers. Macromolecules 1994, 27, 4063-75.
176. Lai, C. T.; Shi, A. Binary blends of diblock copolymers: an effective route to novel bicontinuous phases. Macromol. Theor. Simul. 2021, 30, 2100019.
177. Xie, O.; Cohen, A. E.; Bazant, M. Z.; Olsen, B. D. Learning nature’s assembly language with polymers. Proc. Natl. Acad. Sci. U. S. A. 2026, 123, e2519094123.
178. Alward, D. B.; Kinning, D. J.; Thomas, E. L.; Fetters, L. J. Effect of arm number and arm molecular weight on the solid-state morphology of poly(styrene-isoprene) star block copolymers. Macromolecules 1986, 19, 215-24.
179. Thomas, E. L.; Alward, D. B.; Kinning, D. J.; Martin, D. C.; Handlin, D. L.; Fetters, L. J. Ordered bicontinuous double-diamond structure of star block copolymers: a new equilibrium microdomain morphology. Macromolecules 1986, 19, 2197-202.
180. Kinning, D. J.; Thomas, E. L.; Alward, D. B.; Fetters, L. J.; Handlin, D. L. Sharpness of the functionality-induced structural transition in poly(styrene-isoprene) star block copolymers. Macromolecules 1986, 19, 1288-90.
181. Likhtman, A. E.; Semenov, A. N. Stability of the OBDD structure for diblock copolymer melts in the strong segregation limit. Macromolecules 1994, 27, 3103-6.
182. Olmsted, P. D.; Milner, S. T. Strong-segregation theory of bicontinuous phases in block copolymers. Phys. Rev. Lett. 1995, 74, 829.
183. Hajduk, D. A.; Harper, P. E.; Gruner, S. M.; Honeker, C. C.; Thomas, E. L.; Fetters, L. J. A reevaluation of bicontinuous cubic phases in starblock copolymers. Macromolecules 1995, 28, 2570-3.
184. Susca, E. M.; Beaucage, P. A.; Thedford, R. P.; et al. Preparation of macroscopic block-copolymer-based gyroidal mesoscale single crystals by solvent evaporation. Adv. Mater. 2019, 31, e1902565.
185. Lin, C.; Higuchi, T.; Chen, H.; Tsai, J.; Jinnai, H.; Hashimoto, T. Stabilizing the ordered bicontinuous double diamond structure of diblock copolymer by configurational regularity. Macromolecules 2018, 51, 4049-58.
186. Chu, C.; Lin, W.; Tsai, J.; et al. Order-order transition between equilibrium ordered bicontinuous nanostructures of double diamond and double gyroid in stereoregular block copolymer. Macromolecules 2012, 45, 2471-7.
187. Chu, C. Y.; Jiang, X.; Jinnai, H.; et al. Real-space evidence of the equilibrium ordered bicontinuous double diamond structure of a diblock copolymer. Soft Matter 2015, 11, 1871-6.
188. Chu, C. Y.; Jiang, X.; Jinnai, H.; et al. Correction: real-space evidence of the equilibrium ordered bicontinuous double diamond structure of a diblock copolymer. Soft Matter 2015, 11, 4142.
189. Winey, K. I.; Thomas, E. L.; Fetters, L. J. The ordered bicontinuous double-diamond morphology in diblock copolymer/homopolymer blends. Macromolecules 1992, 25, 422-8.
190. Hsueh, H. Y.; Ling, Y. C.; Wang, H. F.; et al. Shifting networks to achieve subgroup symmetry properties. Adv. Mater. 2014, 26, 3225-9.
191. An, T. H.; La, Y.; Cho, A.; et al. Solution self-assembly of block copolymers containing a branched hydrophilic block into inverse bicontinuous cubic mesophases. ACS Nano 2015, 9, 3084-96.
192. Cho, A.; La, Y.; Shin, T. J.; Park, C.; Kim, K. T. Structural requirements of block copolymers for self-assembly into inverse bicontinuous cubic mesophases in solution. Macromolecules 2016, 49, 4510-9.
193. La, Y.; An, T. H.; Shin, T. J.; Park, C.; Kim, K. T. A morphological transition of inverse mesophases of a branched-linear block copolymer guided by using cosolvents. Angew. Chem. Int. Ed. Engl. 2015, 54, 10483-7.
194. Finnefrock, A. C.; Ulrich, R.; Du, Chesne. A.; et al. Metal oxide containing mesoporous silica with bicontinuous “plumber’s nightmare” morphology from a block copolymer-hybrid mesophase. Angew. Chem. Int. Ed. 2001, 40, 1207-11. https://onlinelibrary.wiley.com/doi/abs/10.1002/1521-3773%2820010401%2940%3A7%3C1207%3A%3AAID-ANIE1207%3E3.0.CO%3B2-S.
195. Finnefrock, A. C.; Ulrich, R.; Toombes, G. E.; Gruner, S. M.; Wiesner, U. The plumber’s nightmare: a new morphology in block copolymer-ceramic nanocomposites and mesoporous aluminosilicates. J. Am. Chem. Soc. 2003, 125, 13084-93.
196. Toombes, G. E. S.; Finnefrock, A. C.; Tate, M. W.; Ulrich, R.; Wiesner, U.; Gruner, S. M. A re-evaluation of the morphology of a bicontinuous block copolymer-ceramic material. Macromolecules 2007, 40, 8974-82.
197. Robbins, S. W.; Beaucage, P. A.; Sai, H.; et al. Block copolymer self-assembly-directed synthesis of mesoporous gyroidal superconductors. Sci. Adv. 2016, 2, e1501119.
198. Robbins, S. W.; Sai, H.; DiSalvo, F. J.; Gruner, S. M.; Wiesner, U. Monolithic gyroidal mesoporous mixed titanium-niobium nitrides. ACS Nano 2014, 8, 8217-23.
199. Cao, X.; Xu, D.; Yao, Y.; Han, L.; Terasaki, O.; Che, S. Interconversion of triply periodic constant mean curvature surface structures: from double diamond to single gyroid. Chem. Mater. 2016, 28, 3691-702.
200. Bao, C.; Chen, H.; Che, S.; Han, L. Direct imaging of the structural transition and interconversion of macroporous bicontinuous diamond-surface structure. Microporous Mesoporous Mater. 2021, 320, 111084.
201. Bao, C.; Che, S.; Han, L. Discovery of single gyroid structure in self-assembly of block copolymer with inorganic precursors. J. Hazard. Mater. 2021, 402, 123538.
202. Matsen, M. W. Cylinder↔gyroid epitaxial transitions in complex polymeric liquids. Phys. Rev. Lett. 1998, 80, 4470-3.
203. Sheng, Q.; Chen, H.; Mao, W.; Cui, C.; Che, S.; Han, L. Self-assembly of single-diamond-surface networks. Angew. Chem. Int. Ed. Engl. 2021, 60, 15236-42.
204. Karpov, D.; Djeghdi, K.; Holler, M.; et al. High-resolution three-dimensional imaging of topological textures in nanoscale single-diamond networks. Nat. Nanotechnol. 2024, 19, 1499-506.
205. Djeghdi, K.; Karpov, D.; Abdollahi, S. N.; et al. Block copolymer-directed single-diamond hybrid structures derived from X-ray nanotomography. ACS Nano 2024, 18, 26503-13.
206. Guillamat, P.; Mirza, W.; Bal, P. K.; et al. Guidance of cellular nematic elastomers into shape-programmable living surfaces. Science 2026, 392, 317-23.
207. Wang, S.; Li, Y.; Yang, B.; et al. Evolution of curvatures between lamellar and bicontinuous phases: formation of saddle-shaped hierarchical lamellar structures in binary self-assembly system. Small 2026, 22, e08085.
208. Wang, S.; Chen, H.; Zhong, T.; et al. Tetragonal gyroid structure from symmetry manipulation: a brand-new member of the gyroid surface family. Chem 2024, 10, 1406-24.
209. Cui, C.; Cao, Y.; Han, L. Deep-learning-assisted understanding of the self-assembly of miktoarm star block copolymers. ACS Nano 2025, 19, 11427-39.
210. Fronzi, M.; Stampfl, C.; Traversa, E. From atoms to systems: machine learning in the clean energy materials revolution. Mater. Renew. Sustain. Energy 2026, 15, 374.
211. Saleh, G.; Manna, L. The predictive power of chemical bonding analysis in materials: a perspective on optoelectronic properties. J. Am. Chem. Soc. 2025, 147, 46705-19.
212. Shuang, F.; Wei, Z.; Liu, K.; Gao, W.; Dey, P. Universal machine learning interatomic potentials poised to supplant DFT in modeling general defects in metals and random alloys. Mach. Learn.: Sci. Technol. 2025, 6, 030501.
213. Su, L.; Lu, F.; Li, Y.; et al. Gyroid liquid crystals as quasi-solid-state electrolytes toward ultrastable zinc batteries. ACS Nano 2024, 18, 7633-43.
214. Tang, C.; Lu, W.; Zhang, Y.; et al. Toward ultrahigh rate and cycling performance of cathode materials of sodium ion battery by introducing a bicontinuous porous structure. Adv. Mater. 2024, 36, e2402005.
215. Xiang, L.; Yuan, S.; Wang, F.; et al. Porous polymer cubosomes with ordered single primitive bicontinuous architecture and their sodium-iodine batteries. J. Am. Chem. Soc. 2022, 144, 15497-508.
216. Reyes, C. F.; Ha, S.; Kim, K. T. Synthesis and applications of polymer cubosomes and hexosomes. J. Polym. Sci. 2023, 61, 1196-213.
217. Li, Q.; Chen, C.; Li, C.; et al. Ordered bicontinuous mesoporous polymeric semiconductor photocatalyst. ACS Nano 2020, 14, 13652-62.
218. Wang, C.; Lu, W.; Wang, J.; Che, S.; Lu, A.; Han, L. Synthesis of ordered mesoporous crystalline boron phosphate scaffold with double diamond surface structure. Sci. China Chem. 2025, 68, 590-600.
219. Moore, W.; Shoji, S.; Tsaur, L.; et al. Asymmetric porous catalyst structures for low-temperature photocatalytic dry reforming of methane. ACS Nano 2025, 19, 23817-28.
220. Cherevan, A. S.; Robbins, S.; Dieterle, D.; Gebhardt, P.; Wiesner, U.; Eder, D. Ordered gyroidal tantalum oxide photocatalysts: eliminating diffusion limitations and tuning surface barriers. Nanoscale 2016, 8, 16694-701.
221. Li, W.; Ding, J.; Chen, X.; Wang, Y.; Song, X.; Zhang, S. A 3D-printed CuNi alloy catalyst with a triply periodic minimal surface for the reverse water-gas shift reaction. J. Mater. Chem. A 2023, 12, 314-20.
222. Asmat, H.; Paul, P.; Mclaren, F.; et al. Electrified reformer for syngas production - additive manufacturing of coated microchannel monolithic reactor. Appl. Catal. B Environ. 2025, 361, 124640.
223. Guo, Z. W.; Chen, C. C.; Huang, Y. T.; Fuh, Y. K. Self-powered fire alarm system based on Ti3C2Tx MXene/PVP/piezoelectric fibers multilayers embedded with additively manufactured TPMS spacers with tunable stiffness. Chem. Eng. J. 2025, 503, 158423.
224. Noroozi, R.; Quiquero, D.; Huang, Y. Y. S.; Shi, H. H. Hierarchical multi-material architectures with gradient design for dynamic-range flexible tactile sensing. Adv. Mater. Technol. 2026, e02632.
225. Pang, Y.; Zhu, X.; Liu, S.; Lee, C. A natural gradient biological-enabled multimodal triboelectric nanogenerator for driving safety monitoring. ACS Nano 2023, 17, 21878-92.
226. Imanian, M. E.; Kardan-Halvaei, M.; Nasrollahi, F.; Imanian, A.; Montazerian, H.; Nasrollahi, V. 3D printed flexible wearable sensors based on triply periodic minimal surface structures for biomonitoring applications. Smart Mater. Struct. 2023, 32, 015015.
227. Moeinnia, H.; Ganzert, C.; Schubert, L.; Kim, W. S. Streamlined custom manufacturing for optimized 3D printed prostheses through 3D pressure mapping. Biosens. Bioelectron. 2026, 302, 118560.
228. Li, Z.; Feng, D.; Li, B.; et al. Ultra-wide range, high sensitivity piezoresistive sensor based on triple periodic minimum surface construction. Small 2023, 19, e2301378.
229. Han, J.; Li, Z.; Kong, S.; Tang, S.; Feng, D.; Li, B. Wide-response-range and high-sensitivity piezoresistive sensors with triple periodic minimal surface (TPMS) structures for wearable human-computer interaction systems. Compos. Part. B-Eng. 2024, 287, 111840.
230. Han, J.; Li, Z.; Kong, S.; et al. Enhanced sensitivity and broadband response in porous triple periodic minimal surface piezoresistive sensors for telemedicine applications. Chem. Eng. J. 2024, 500, 156989.
231. Tang, C.; Zhu, J.; Wu, X.; Peng, Q.; Wang, X. Experimental investigation on multi-factor optimization of triply periodic minimal surface structured micro-generators via response surface methodology. Energy 2026, 361, 142181.
232. Zhao, P.; Zhang, Y.; Qiao, Z. Research progress of 3D-printed anti-infective bone tissue engineering scaffolds based on triply periodic minimal surface structures. APL Bioeng 2026, 10, 021506.
233. Ramírez-Solana, D.; Sangiorgio, V.; Redondo, J.; Gulzari, M. Sound diffusion properties of triply periodic minimal surfaces using three-dimensional FDTD simulations. Appl. Math. Model. 2026, 157, 116867.
234. Roohani, I.; Entezari, A.; Zreiqat, H. Liquid crystal display technique (LCD) for high resolution 3D printing of triply periodic minimal surface lattices bioceramics. Addit. Manuf. 2023, 74, 103720.
235. Papkov, V.; Tartakovsky, L.; Pashchenko, D. Triply periodic minimal surfaces as catalyst carriers of compact reformers for hydrogen production and storage systems: recent advances and future perspectives. Renew. Sustain. Energy Rev. 2026, 237, 117070.
236. Karami, Z.; Hamidi, M. Cubosomes: remarkable drug delivery potential. Drug Discov. Today 2016, 21, 789-801.
237. Hur, K.; Hennig, R. G.; Wiesner, U. Exploring periodic bicontinuous cubic network structures with complete phononic bandgaps. J. Phys. Chem. C 2017, 121, 22347-52.
238. Flavell, W.; Neophytou, A.; Demetriadou, A.; Albrecht, T.; Chakrabarti, D. Programmed self-assembly of single colloidal gyroids for chiral photonic crystals. Adv. Mater. 2023, 35, e2211197.
239. Liu, Y.; Zhou, Q.; Yu, H.; et al. Increasing the accessibility of internal catalytic sites in covalent organic frameworks by introducing a bicontinuous mesostructure. Angew. Chem. Int. Ed. Engl. 2024, 63, e202400985.
240. Li, C.; Pan, Y.; Xiao, T.; et al. Metal organic framework cubosomes. Angew. Chem. Int. Ed. Engl. 2023, 62, e202215985.
241. Zhang, Y.; Zhang, J.; Yang, W.; Che, S.; Cao, Y.; Han, L. Chirality manipulation of 3D printed gyroidal scaffolds towards mechanical properties enhancement. Addit. Manuf. 2024, 96, 104551.
242. Zhang, Y.; Zhang, J.; Chen, X.; et al. Mechanical properties of 3D-printed polymeric cellular structures based on bifurcating triply periodic minimal surfaces. Adv. Eng. Mater. 2025, 27, 2402507.
243. Zhang, Y.; Zhang, J.; Zhao, X.; et al. Mechanical behaviors regulation of triply periodic minimal surface structures with crystal twinning. Addit. Manuf. 2022, 58, 103036.
244. Tang, C.; Zhang, W.; Zhang, Y.; et al. Bicontinuous structure mediated microstructural engineering of hard carbon for enhanced sodium storage. Adv. Mater. 2026, 38, e11632.
245. Liu, C.; Yoshio, M. Topology-controlled proton transport in thermotropic liquid-crystalline acid-base complexes. Chem. Mater. 2026, 38, 10106-17.
246. Jennings, J.; Pabst, G. Multiple routes to bicontinuous cubic liquid crystal phases discovered by high-throughput self-assembly screening of multi-tail lipidoids. Small 2023, 19, e2206747.
247. Chen, Z.; Huang, Q.; Song, Y.; et al. Cubosomes-assisted transdermal delivery of doxorubicin and indocyanine green for chemo-photothermal combination therapy of melanoma. Biomed. Pharmacother. 2023, 166, 115316.
248. Kibsgaard, J.; Chen, Z.; Reinecke, B. N.; Jaramillo, T. F. Engineering the surface structure of MoS2 to preferentially expose active edge sites for electrocatalysis. Nat. Mater. 2012, 11, 963-9.
249. Morey, M.; Davidson, A.; Stucky, G. Silica-based, cubic mesostructures: synthesis, characterization and relevance for catalysis. J. Porous Mater. 1998, 5, 195-204.
250. Niu, T.; Li, R.; Chen, X.; et al. Revealing the underlying mechanisms in performance enhancement of shellular lattice electrodes during anion exchange membrane water electrolysis process. Adv. Sci. (Weinh). 2026, e77317.
251. Liao, N.; Zhao, J.; Luo, J. 3D-printed metal electrodes with enhanced bubble removal for efficient water electrolysis. Nano Lett. 2025, 25, 9551-9.
252. Crossland, E. J.; Kamperman, M.; Nedelcu, M.; et al. A bicontinuous double gyroid hybrid solar cell. Nano Lett. 2009, 9, 2807-12.
253. Li, Y.; Zhang, M.; Xu, Z.; et al. Biomimetic porous carbon of marine sponge for high performance cathode of Li-S battery. Adv. Mater. 2026, 38, e73073.
254. Werner, J. G.; Rodríguez-Calero, G. G.; Abruña, H. D.; Wiesner, U. Block copolymer derived 3-D interpenetrating multifunctional gyroidal nanohybrids for electrical energy storage. Energy. Environ. Sci. 2018, 11, 1261-70.
255. Zhou, Z.; Lalwani, A. R.; Sun, X.; et al. Monolithic gyroidal solid oxide cells by additive manufacturing. Nat. Energy 2025, 10, 962-70.
256. Xie, W.; Huang, X.; Zhu, C.; et al. A versatile synthesis platform based on polymer cubosomes for a library of highly ordered nanoporous metal oxides particles. Adv. Mater. 2024, 36, e2313920.
257. Alzoubi, M. A.; Al-Ketan, O.; Muthusamy, J.; Sasmito, A. P.; Poncet, S. Mixing performance of T-shape micromixers equipped with 3D printed gyroid matrices: a numerical evaluation. Results Eng. 2023, 17, 100811.
258. Tang, W.; Zhou, H.; Zeng, Y.; et al. Analysis on the convective heat transfer process and performance evaluation of triply periodic minimal surface (TPMS) based on diamond, gyroid and Iwp. Int. J. Heat Mass Transfer. 2023, 201, 123642.
259. Wang, H.; Zheng, S.; Liu, G.; et al. Influences of the flow rate and fluid volume in air-kerosene cross-flow heat exchangers using gyroid-typed triply periodic minimal surfaces. Appl. Therm. Eng. 2025, 263, 125336.
260. Wang, H.; Zhao, C.; Liu, W.; Liu, Z.; Bian, H.; Zhang, K. Advances in triply periodic minimal surface structures for thermal management systems: A comprehensive review. Appl. Therm. Eng. 2025, 279, 127481.
261. Zhao, R.; Yuan, K.; Deng, J.; et al. Enhanced hydrogen storage performance by incorporating triply periodic minimal surface into metal hydride reactor. Renew. Energy 2026, 270, 125896.
262. Chen, J.; Liu, X.; Li, Y.; et al. Numerical and experimental investigation of TPMS-structured cold plates for electronic device cooling. Appl. Energy 2025, 401, 126745.
263. Li, S.; Zhang, H.; Ma, S.; et al. Fundamentals, classification of photonic crystals and their applications in textiles: a review. Adv. Fiber Mater. 2026, 8, 1759-803.
264. Meng, Z.; Miao, S.; Liu, Y.; et al. Photonic crystal-based structural color switches. Mater. Horiz. 2025, 12, 8380-408.
265. Li, P.; Wu, J.; Chen, K.; Dong, J.; Hu, Y. Advances in the fabrication of multiple stopband photonic crystal microparticles. CrystEngComm 2025, 27, 4796-809.
266. Lv, J.; Gao, X.; Tang, Z. Bioinspired chiral photonic crystals. Sci. China Mater. 2025, 68, 979-97.
267. Dolan, J. A.; Wilts, B. D.; Vignolini, S.; Baumberg, J. J.; Steiner, U.; Wilkinson, T. D. Optical properties of gyroid structured materials: from photonic crystals to metamaterials. Adv. Opt. Mater. 2015, 3, 12-32.
268. Zhang, W.; Min, J.; Wang, H.; et al. Printing of 3D photonic crystals in titania with complete bandgap across the visible spectrum. Nat. Nanotechnol. 2024, 19, 1813-20.
269. Jo, S.; Park, H.; Lee, J.; et al. Visible photonic bandgap configured by non-affine block copolymer gyroid. Adv. Opt. Mater. 2026, 14, e02817.
270. Vignolini, S.; Yufa, N. A.; Cunha, P. S.; et al. A 3D optical metamaterial made by self-assembly. Adv. Mater. 2012, 24, OP23-7.
271. Park, H.; Jo, S.; Kang, B.; et al. Block copolymer gyroids for nanophotonics: significance of lattice transformations. Nanophotonics 2022, 11, 2583-615.
273. Lu, L.; Fu, L.; Joannopoulos, J. D.; Soljačić, M. Weyl points and line nodes in gyroid photonic crystals. Nat. Photon. 2013, 7, 294-9.
274. Fang, C.; Lu, L.; Liu, J.; Fu, L. Topological semimetals with helicoid surface states. Nat. Phys. 2016, 12, 936-41.
275. Lu, L.; Wang, Z.; Ye, D.; et al. TOPOLOGICAL MATTER. Experimental observation of Weyl points. Science 2015, 349, 622-4.
276. Liu, B.; Johnson, S. G.; Joannopoulos, J. D.; Lu, L. Generalized gilat-raubenheimer method for density-of-states calculation in photonic crystals. J. Opt. 2018, 20, 044005.
277. Lu, L.; Gao, H.; Wang, Z. Topological one-way fiber of second Chern number. Nat. Commun. 2018, 9, 5384.
279. Kim, H.; Cheng, H.; Lu, L.; Murakami, S. Theoretical analysis of glide-Z2 magnetic topological photonic crystals. Opt. Express 2021, 29, 31164-78.
280. Sam, S.; Say, S.; Sang, L.; Nakatsugawa, H. Nanostructuring thermoelectric materials using phononic crystals and reduction in lattice thermal conductivity. Next Energy 2026, 11, 100550.
281. Guo, L.; Zhao, S.; Guo, Z.; Zhang, Y.; Yang, J.; Kitipornchai, S. Phase transition-based tunable phononic crystals and metamaterials: a review. Thin-Walled Struct. 2026, 218, 113984.
282. Bahrami, A.; Motaei, F. A review of phononic-crystal-based energy harvesters. Prog. Energy 2025, 7, 012002.
283. Wu, B.; Jiang, W.; Jiang, J.; et al. Wave manipulation in intelligent metamaterials: recent progress and prospects. Adv. Funct. Mater. 2024, 34, 2316745.
284. He, Y.; Wu, Y.; Qin, Y.; et al. Research on the control method of Bragg bandgap characteristics of phononic crystal beams based on Cantor fractals. J. Phys. D: Appl. Phys. 2026, 59, 015301.
285. Wang, Y.; Li, D. Design of a defect containing bi-material nested structure phononic crystal with adjustable band gap. Appl. Acoust. 2025, 240, 110930.
286. Chen, Y.; Liang, S.; Lan, Z.; Gu, Z.; Su, Z.; Zhu, J. A triply periodic minimal surface-based acoustic crystal with double-zero index. Mater. Horiz. 2026, 13, 6428-33.
287. Wu, Y.; Qi, X.; Sun, L.; Wang, B.; Wang, P.; Li, W. Acoustic performance of micro-perforated plate sandwich structure based on triply periodic minimal surfaces. Mater. Today Commun. 2025, 49, 114249.
288. Chen, X.; Sun, G.; Zhu, J.; Kang, W.; Shang, D.; Deng, Z. Influence of structural parameters on mechanical properties of triply periodic minimal surface structure. Metals 2023, 13, 285.
289. Chatzigeorgiou, C.; Piotrowski, B.; Chemisky, Y.; Laheurte, P.; Meraghni, F. Numerical investigation of the effective mechanical properties and local stress distributions of TPMS-based and strut-based lattices for biomedical applications. J. Mech. Behav. Biomed. Mater. 2022, 126, 105025.
290. Barber, H.; Kelly, C. N.; Nelson, K.; Gall, K. Compressive anisotropy of sheet and strut based porous Ti-6Al-4V scaffolds. J. Mech. Behav. Biomed. Mater. 2021, 115, 104243.
291. Zhang, L.; Feih, S.; Daynes, S.; et al. Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading. Addit. Manuf. 2018, 23, 505-15.
292. Vijayavenkataraman, S.; Zhang, L.; Zhang, S.; Fuh, J. Y. H.; Lu, W. Triply periodic minimal surfaces sheet scaffolds for tissue engineering applications: an optimization approach toward biomimetic scaffold design. ACS Appl. Bio. Mater. 2018, 1, 259-69.
293. Al-Ketan, O.; Rowshan, R.; Abu Al-Rub, R. K. Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials. Addit. Manuf. 2018, 19, 167-83.
294. Maskery, I.; Aboulkhair, N.; Aremu, A.; Tuck, C.; Ashcroft, I. Compressive failure modes and energy absorption in additively manufactured double gyroid lattices. Addit. Manuf. 2017, 16, 24-9.
