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Particle shape plays a critical role in the result of their assembly, often leading to complex NP superlattices resulting from locally dense particle packing. Right bipyramids (rBPs), with their distinct 110.9\u00b0 dihedral angles, introduce geometric frustration that prevents conventional crystalline packing. Here, we combine electron microscopy, geometric arguments, and Monte Carlo simulations to investigate the geometrically frustrated assembly of rBPs under drop-casting conditions. We show that rBPs reproducibly self-assemble into energetically favorable, quasi-spherical superstructures composed of 130 rBPs (130-rBP) with hierarchical internal order, formed through a stepwise self-assembly pathway involving intermediates comprising 8 and 35 rBPs. These 130-rBP superstructures serve as fundamental building blocks for larger complex superstructures such as dimers (225 rBPs) and trimers (300 rBPs), in which multiple 130-rBP motifs remain clearly discernible but overlap extensively. Despite their high degree of local order, these assemblies do not form bulk crystals. Monte Carlo simulations of the assembly process predict the observed superstructures, both in the presence and absence of an underlying surface, demonstrating that the assemblies are driven by the unique geometry of the particles rather than the assembly environment. These results reveal a frustrated assembly mechanism in which the particle geometry promotes the formation of highly ordered, albeit noncrystalline, superstructures by inhibiting the unbounded growth of crystalline superlattice structures.<\/jats:p>","DOI":"10.1021\/acsnano.6c01985","type":"journal-article","created":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T09:14:23Z","timestamp":1784711663000},"page":"23729-23739","source":"Crossref","is-referenced-by-count":0,"title":["Frustrated Assembly\nof Nanoscale Bipyramids into Uniquely\nOrdered Superstructures"],"prefix":"10.1021","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5477-6299","authenticated-orcid":true,"given":"Daniel","family":"Garci\u0301a-Lojo","sequence":"first","affiliation":[{"name":"CINBIO, Universidade de Vigo , , Campus Universitario as Lagoas, Marcosende ,","place":["Vigo, Spain, 36310"]},{"name":"Galicia Sur Health Research Institute (IIS Galicia Sur) , ,","place":["Vigo, Spain, 36310"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5775-7213","authenticated-orcid":true,"given":"Nan","family":"Cheng","sequence":"additional","affiliation":[{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5709-7259","authenticated-orcid":true,"given":"Timothy C.","family":"Moore","sequence":"additional","affiliation":[{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6313-2340","authenticated-orcid":true,"given":"Rafael","family":"Contreras-Ca\u0301ceres","sequence":"additional","affiliation":[{"name":"University of Almeri\u0301a , , ,","place":["Almeri\u0301a, Spain, 04120"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiongyang","family":"Chen","sequence":"additional","affiliation":[{"name":"University of Antwerp , , ,","place":["Antwerp, Belgium, 2020"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eva","family":"Bladt","sequence":"additional","affiliation":[{"name":"University of Antwerp , , ,","place":["Antwerp, Belgium, 2020"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8885-788X","authenticated-orcid":true,"given":"Benito","family":"Rodri\u0301guez-Gonzalez","sequence":"additional","affiliation":[{"name":"CINBIO, Universidade de Vigo , , Campus Universitario as Lagoas, Marcosende ,","place":["Vigo, Spain, 36310"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4614-1699","authenticated-orcid":true,"given":"Jorge","family":"Pe\u0301rez-Juste","sequence":"additional","affiliation":[{"name":"CINBIO, Universidade de Vigo , , Campus Universitario as Lagoas, Marcosende ,","place":["Vigo, Spain, 36310"]},{"name":"Galicia Sur Health Research Institute (IIS Galicia Sur) , ,","place":["Vigo, Spain, 36310"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Sun","sequence":"additional","affiliation":[{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4249-8017","authenticated-orcid":true,"given":"Sara","family":"Bals","sequence":"additional","affiliation":[{"name":"University of Antwerp , , ,","place":["Antwerp, Belgium, 2020"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6647-1353","authenticated-orcid":true,"given":"Luis M.","family":"Liz-Marza\u0301n","sequence":"additional","affiliation":[{"name":"CINBIO, Universidade de Vigo , , Campus Universitario as Lagoas, Marcosende ,","place":["Vigo, Spain, 36310"]},{"name":"CIC biomaGUNE, Basque Research and Technology Alliance (BRTA) , ,","place":["Donostia-San Sebastia\u0301n, Spain, 20014"]},{"name":"Centro de Investigacio\u0301n Biome\u0301dica en Red de Bioingenieri\u0301a, Biomateriales y Nanomedicina (CIBERBBN) , ,","place":["Donostia-San Sebastia\u0301n, Spain, 20014"]},{"name":"Ikerbasque, Basque Foundation for Science , ,","place":["Bilbao, Spain, 48009"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7197-0085","authenticated-orcid":true,"given":"Sharon C.","family":"Glotzer","sequence":"additional","affiliation":[{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]},{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]},{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoming","family":"Mao","sequence":"additional","affiliation":[{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6864-5804","authenticated-orcid":true,"given":"Nicholas A.","family":"Kotov","sequence":"additional","affiliation":[{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]},{"name":"University of Michigan , , , ,","place":["Ann Arbor, Michigan, United States, 48109"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1091-1364","authenticated-orcid":true,"given":"Isabel","family":"Pastoriza-Santos","sequence":"additional","affiliation":[{"name":"CINBIO, Universidade de Vigo , , Campus Universitario as Lagoas, Marcosende ,","place":["Vigo, Spain, 36310"]},{"name":"Galicia Sur Health Research Institute (IIS Galicia Sur) , ,","place":["Vigo, Spain, 36310"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,7,22]]},"reference":[{"issue":"7","key":"2026090306574582000_cit1","doi-asserted-by":"publisher","first-page":"1855","DOI":"10.1021\/acs.accounts.9b00213","article-title":"Plasmonic Supercrystals","volume":"52","author":"Garci\u0301a-Lojo","year":"2019","journal-title":"Acc.\nChem. Res."},{"issue":"1","key":"2026090306574582000_cit2","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.nantod.2015.01.006","article-title":"Formation of Supercrystals through\nSelf-Assembly of Polyhedral Nanocrystals","volume":"10","author":"Huang","year":"2015","journal-title":"Nano\nToday"},{"issue":"5","key":"2026090306574582000_cit3","doi-asserted-by":"publisher","first-page":"4976","DOI":"10.1021\/acs.chemrev.1c00482","article-title":"Colloidal Self-Assembly Approaches\nto Smart Nanostructured\nMaterials","volume":"122","author":"Li","year":"2022","journal-title":"Chem. Rev."},{"issue":"8","key":"2026090306574582000_cit4","doi-asserted-by":"publisher","first-page":"3330","DOI":"10.1021\/jacs.1c12335","article-title":"Nanoparticle\nAssembly as a Materials Development Tool","volume":"144","author":"Lee","year":"2022","journal-title":"J.\nAm. Chem. Soc."},{"issue":"5579","key":"2026090306574582000_cit5","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1126\/science.1072086","article-title":"Spontaneous\nOrganization of Single\nCdTe Nanoparticles into Luminescent Nanowires","volume":"297","author":"Tang","year":"2002","journal-title":"Science"},{"issue":"18","key":"2026090306574582000_cit6","doi-asserted-by":"publisher","first-page":"11220","DOI":"10.1021\/acs.chemrev.6b00196","article-title":"Self-Assembly of Colloidal Nanocrystals:\nFrom Intricate Structures to Functional Materials","volume":"116","author":"Boles","year":"2016","journal-title":"Chem. Rev."},{"issue":"16","key":"2026090306574582000_cit7","doi-asserted-by":"publisher","first-page":"6002","DOI":"10.1039\/D0CS00541J","article-title":"Self-Assembly of Anisotropic Nanoparticles\ninto Functional Superstructures","volume":"49","author":"Deng","year":"2020","journal-title":"Chem. Soc.\nRev."},{"issue":"23","key":"2026090306574582000_cit8","doi-asserted-by":"publisher","first-page":"14791","DOI":"10.1021\/acsnano.3c10201","article-title":"Nanocrystal\nAssemblies: Current Advances and Open Problems","volume":"18","author":"Bassani","year":"2024","journal-title":"ACS Nano"},{"issue":"6093","key":"2026090306574582000_cit9","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1126\/science.1220869","article-title":"Predictive Self-Assembly of Polyhedra\ninto Complex Structures","volume":"337","author":"Damasceno","year":"2012","journal-title":"Science"},{"issue":"7274","key":"2026090306574582000_cit10","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1038\/nature08641","article-title":"Disordered, Quasicrystalline and\nCrystalline Phases of Densely Packed Tetrahedra","volume":"462","author":"Haji-Akbari","year":"2009","journal-title":"Nature"},{"issue":"11","key":"2026090306574582000_cit11","doi-asserted-by":"publisher","first-page":"110901","DOI":"10.1063\/1.4962629","article-title":"Perspective:\nGeometrically Frustrated Assemblies","volume":"145","author":"Grason","year":"2016","journal-title":"J. Chem.\nPhys."},{"issue":"2","key":"2026090306574582000_cit12","doi-asserted-by":"publisher","first-page":"025008","DOI":"10.1103\/RevModPhys.93.025008","article-title":"Equilibrium Mechanisms\nof Self-Limiting Assembly","volume":"93","author":"Hagan","year":"2021","journal-title":"Rev. Mod. Phys."},{"issue":"4","key":"2026090306574582000_cit13","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1557\/s43577-024-00698-6","article-title":"Complexity, Disorder,\nand Functionality of Nanoscale Materials","volume":"49","author":"Mao","year":"2024","journal-title":"MRS\nBull."},{"issue":"5","key":"2026090306574582000_cit14","doi-asserted-by":"publisher","first-page":"054601","DOI":"10.1103\/PhysRevE.104.054601","article-title":"Cumulative Geometric Frustration\nin Physical Assemblies","volume":"104","author":"Meiri","year":"2021","journal-title":"Phys. Rev. E"},{"issue":"7","key":"2026090306574582000_cit15","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1038\/nmat4598","article-title":"Morphology Selection\nvia Geometric Frustration in Chiral Filament Bundles","volume":"15","author":"Hall","year":"2016","journal-title":"Nat. Mater."},{"issue":"11","key":"2026090306574582000_cit16","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1038\/nphys4184","article-title":"Geometrical Frustration Yields Fibre Formation in Self-Assembly","volume":"13","author":"Lenz","year":"2017","journal-title":"Nat. Phys."},{"issue":"1","key":"2026090306574582000_cit17","doi-asserted-by":"publisher","first-page":"4925","DOI":"10.1038\/s41467-021-25139-9","article-title":"Frustrated Self-Assembly\nof Non-Euclidean Crystals of Nanoparticles","volume":"12","author":"Serafin","year":"2021","journal-title":"Nat. Commun."},{"issue":"45","key":"2026090306574582000_cit18","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1418159111","article-title":"Understanding Shape Entropy through Local Dense Packing","volume":"111","author":"van Anders","year":"2014","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"issue":"16","key":"2026090306574582000_cit19","doi-asserted-by":"publisher","first-page":"1121","DOI":"10.1103\/PhysRevLett.47.1121","article-title":"Magic Numbers\nfor Sphere Packings:\nExperimental Verification in Free Xenon Clusters","volume":"47","author":"Echt","year":"1981","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"2026090306574582000_cit20","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1107\/S0365110X6200239X","article-title":"A Dense\nNon-Crystallographic Packing of Equal Spheres","volume":"15","author":"Mackay","year":"1962","journal-title":"Acta Crystallogr."},{"issue":"4\u20136","key":"2026090306574582000_cit21","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/S0009-2614(95)01223-0","article-title":"Magic Numbers and Growth Sequences\nof Small Face-Centered-Cubic\nand Decahedral Clusters","volume":"247","author":"Doye","year":"1995","journal-title":"Chem. Phys. Lett."},{"issue":"13","key":"2026090306574582000_cit22","doi-asserted-by":"publisher","first-page":"11152","DOI":"10.1021\/acsami.7b19081","article-title":"Seeded Growth\nSynthesis of Gold Nanotriangles:\nSize Control, SAXS Analysis, and SERS Performance","volume":"10","author":"Kuttner","year":"2018","journal-title":"ACS Appl. Mater. Interfaces"},{"issue":"5","key":"2026090306574582000_cit23","doi-asserted-by":"publisher","first-page":"1700114","DOI":"10.1002\/ppsc.201700114","article-title":"High-Yield Synthesis\nof Au@Ag Right Bipyramids and Self-Assembly\ninto Four-Leaf-Clover-like Structures","volume":"35","author":"Ji","year":"2018","journal-title":"Part.\nPart. Syst. Charact"},{"issue":"8","key":"2026090306574582000_cit24","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1002\/jrs.6677","article-title":"Morphological\nEffect on Core@shell AuAg Nanoparticles for Detecting P-aminothiophenol\nDimerization by Surface-enhanced Raman Spectroscopy","volume":"55","author":"de la Cabeza Ferna\u0301ndez","year":"2024","journal-title":"J. Raman Spectrosc."},{"issue":"25","key":"2026090306574582000_cit25","doi-asserted-by":"publisher","first-page":"13522","DOI":"10.1021\/acs.jpcc.7b12379","article-title":"Multimode Electron Tomography as\na Tool to Characterize the Internal Structure and Morphology of Gold\nNanoparticles","volume":"122","author":"Winckelmans","year":"2018","journal-title":"J. Phys. Chem. C"},{"issue":"31","key":"2026090306574582000_cit26","doi-asserted-by":"publisher","first-page":"15859","DOI":"10.1021\/jp401566m","article-title":"Kinetic and Thermodynamic Modified\nWulff Constructions for Twinned Nanoparticles","volume":"117","author":"Ringe","year":"2013","journal-title":"J. Phys. Chem. C"},{"key":"2026090306574582000_cit27","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1023\/A:1015847520094","article-title":"Mackay,\nAnti-Mackay, Double-Mackay, Pseudo-Mackay, and Related Icosahedral\nShell Clusters 1","volume":"13","author":"Kuo","year":"2002","journal-title":"Struct. Chem."},{"issue":"6","key":"2026090306574582000_cit28","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1524875113","article-title":"Clusters of Polyhedra in Spherical Confinement","volume":"113","author":"Teich","year":"2016","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026090306574582000_cit29","volume-title":"Introduction to Crystallography","author":"Sands","year":"2012"},{"issue":"5","key":"2026090306574582000_cit30","doi-asserted-by":"publisher","first-page":"054132","DOI":"10.1103\/PhysRevE.110.054132","article-title":"Geometrically Frustrated\nSelf-Assembly of Hyperbolic\nCrystals from Icosahedral Nanoparticles","volume":"110","author":"Cheng","year":"2024","journal-title":"Phys.\nRev. E"},{"issue":"30","key":"2026090306574582000_cit31","doi-asserted-by":"publisher","first-page":"14843","DOI":"10.1073\/pnas.1905929116","article-title":"Entropic Colloidal\nCrystallization Pathways via Fluid\u2013Fluid Transitions and Multidimensional\nPrenucleation Motifs","volume":"116","author":"Lee","year":"2019","journal-title":"Proc. Natl. Acad. Sci.\nU. S. A."},{"issue":"4","key":"2026090306574582000_cit32","doi-asserted-by":"publisher","first-page":"041010","DOI":"10.1103\/PhysRevX.13.041010","article-title":"Dispersed, Condensed, and Self-Limiting\nStates of Geometrically Frustrated Assembly","volume":"13","author":"Hackney","year":"2023","journal-title":"Phys. Rev. X"},{"issue":"14","key":"2026090306574582000_cit33","doi-asserted-by":"publisher","first-page":"147401","DOI":"10.1103\/PhysRevLett.134.147401","article-title":"Statistical Mechanics\nof Frustrated Assemblies and Incompatible Graphs","volume":"134","author":"Ortiz-Tava\u0301rez","year":"2025","journal-title":"Phys. Rev. Lett."},{"issue":"13","key":"2026090306574582000_cit34","doi-asserted-by":"publisher","first-page":"2209","DOI":"10.1021\/jz401269w","article-title":"Au@Ag Nanoparticles:\nHalides Stabilize {100} Facets","volume":"4","author":"Go\u0301mez-Gran\u0303a","year":"2013","journal-title":"J. Phys. Chem.\nLett."},{"issue":"20","key":"2026090306574582000_cit35","doi-asserted-by":"publisher","first-page":"3882","DOI":"10.1002\/adma.200800613","article-title":"Synthesis of Complex Au\/Ag Nanorods by Controlled Overgrowth","volume":"20","author":"Park","year":"2008","journal-title":"Adv. Mater."},{"key":"2026090306574582000_cit36","doi-asserted-by":"publisher","first-page":"109363","DOI":"10.1016\/j.commatsci.2019.109363","article-title":"HOOMD-Blue:\nA Python Package for\nHigh-Performance Molecular Dynamics and Hard Particle Monte Carlo\nSimulations","volume":"173","author":"Anderson","year":"2020","journal-title":"Comput. Mater. Sci."},{"key":"2026090306574582000_cit37","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.cpc.2016.02.024","article-title":"Scalable Metropolis Monte Carlo for\nSimulation of Hard Shapes","volume":"204","author":"Anderson","year":"2016","journal-title":"Comput. Phys. 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