{"id":"https://openalex.org/W7204458385","doi":"https://doi.org/10.64336/001c.168714","title":"Why viruses build icosahedra: a quantitative framework for capsid architecture and nanocage design","display_name":"Why viruses build icosahedra: a quantitative framework for capsid architecture and nanocage design","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204458385","doi":"https://doi.org/10.64336/001c.168714"},"language":"en","primary_location":{"id":"doi:10.64336/001c.168714","doi":"https://doi.org/10.64336/001c.168714","is_oa":true,"landing_page_url":"https://doi.org/10.64336/001c.168714","pdf_url":"https://jhss.scholasticahq.com/article/168714.pdf","source":{"id":"https://openalex.org/S5407008444","display_name":"Journal of High School Science","issn_l":"2575-6206","issn":["2575-6206"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High School Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://jhss.scholasticahq.com/article/168714.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148468216","display_name":"Ethan Chang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ethan Chang","raw_affiliation_strings":["Aragon High School, 900 Alameda de las Pulgas, San Mateo, CA 94402-3357, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aragon High School, 900 Alameda de las Pulgas, San Mateo, CA 94402-3357, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148468216"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.56580521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.3052000105381012,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.3052000105381012,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11048","display_name":"Bacteriophages and microbial interactions","score":0.07580000162124634,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10044","display_name":"Protein Structure and Dynamics","score":0.03700000047683716,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/viral-capsid","display_name":"viral capsid","score":0.8640000224113464},{"id":"https://openalex.org/keywords/icosahedral-symmetry","display_name":"icosahedral symmetry","score":0.9919999837875366},{"id":"https://openalex.org/keywords/euler-s-formula","display_name":"Euler's formula","score":0.7440000176429749},{"id":"https://openalex.org/keywords/angular-deficit","display_name":"angular deficit","score":0.8600000143051147},{"id":"https://openalex.org/keywords/curvature-distribution","display_name":"curvature distribution","score":0.6940000057220459},{"id":"https://openalex.org/keywords/viral-evolution","display_name":"viral evolution","score":0.32600000500679016}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.7128999829292297},{"id":"https://openalex.org/C202878990","wikidata":"https://www.wikidata.org/wiki/Q830465","display_name":"Capsid","level":3,"score":0.5595999956130981},{"id":"https://openalex.org/C113709186","wikidata":"https://www.wikidata.org/wiki/Q5986738","display_name":"Icosahedral symmetry","level":2,"score":0.5382000207901001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47929999232292175},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.47209998965263367},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4634000062942505},{"id":"https://openalex.org/C43817857","wikidata":"https://www.wikidata.org/wiki/Q9357547","display_name":"Tessellation (computer graphics)","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4108000099658966},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3912000060081482},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38749998807907104},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C182615771","wikidata":"https://www.wikidata.org/wiki/Q1369386","display_name":"Lytic cycle","level":3,"score":0.36959999799728394},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C70721500","wikidata":"https://www.wikidata.org/wiki/Q177005","display_name":"Computational biology","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3089999854564667},{"id":"https://openalex.org/C118630614","wikidata":"https://www.wikidata.org/wiki/Q1154606","display_name":"DNA origami","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2915000021457672},{"id":"https://openalex.org/C128765274","wikidata":"https://www.wikidata.org/wiki/Q663314","display_name":"Hexagonal crystal system","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.2872999906539917},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2750999927520752},{"id":"https://openalex.org/C2780879997","wikidata":"https://www.wikidata.org/wiki/Q952587","display_name":"Viral protein","level":3,"score":0.2718000113964081},{"id":"https://openalex.org/C160697094","wikidata":"https://www.wikidata.org/wiki/Q1233197","display_name":"Oblique case","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2653000056743622},{"id":"https://openalex.org/C2984241579","wikidata":"https://www.wikidata.org/wiki/Q323611","display_name":"Architectural design","level":3,"score":0.2581000030040741},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C158525013","wikidata":"https://www.wikidata.org/wiki/Q2593739","display_name":"Fusion","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.64336/001c.168714","doi":"https://doi.org/10.64336/001c.168714","is_oa":true,"landing_page_url":"https://doi.org/10.64336/001c.168714","pdf_url":"https://jhss.scholasticahq.com/article/168714.pdf","source":{"id":"https://openalex.org/S5407008444","display_name":"Journal of High School Science","issn_l":"2575-6206","issn":["2575-6206"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High School Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.64336/001c.168714","doi":"https://doi.org/10.64336/001c.168714","is_oa":true,"landing_page_url":"https://doi.org/10.64336/001c.168714","pdf_url":"https://jhss.scholasticahq.com/article/168714.pdf","source":{"id":"https://openalex.org/S5407008444","display_name":"Journal of High School Science","issn_l":"2575-6206","issn":["2575-6206"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High School Science","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204458385.pdf","grobid_xml":"https://content.openalex.org/works/W7204458385.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Many":[0],"viruses":[1],"package":[2],"their":[3],"genomes":[4],"within":[5,212],"protein":[6,270],"shells":[7],"(capsids)":[8],"exhibiting":[9],"icosahedral":[10],"symmetry":[11],"and":[12,17,25,46,76,90,120,142,158,226,235,258,272],"constructed":[13],"from":[14],"recurring":[15],"pentameric":[16],"hexameric":[18],"units.":[19],"This":[20],"study":[21,50],"examines":[22],"whether":[23],"topological":[24],"geometric":[26,210,234],"constraints":[27],"can":[28,79],"help":[29],"explain":[30],"the":[31,49,70,160,181,203,213,216,239,266],"repeated":[32],"emergence":[33],"of":[34,54,215,242,268],"this":[35],"architecture":[36,171],"across":[37],"otherwise":[38],"diverse":[39],"viral":[40,246],"lineages.":[41],"Using":[42],"Euler\u2019s":[43],"polyhedron":[44],"formula":[45],"angular-deficit":[47],"analysis,":[48],"shows":[51],"that":[52],"closure":[53,72,83],"a":[55,207,232],"hexagon-dominated":[56],"lattice":[57],"requires":[58],"twelve":[59],"pentagonal":[60],"units,":[61],"while":[62,248],"additional":[63],"hexagonal":[64],"units":[65],"permit":[66],"expansion":[67],"without":[68],"altering":[69,155],"underlying":[71],"topology.":[73],"Alternative":[74],"tetrahedral":[75],"octahedral":[77],"solutions":[78],"also":[80,264],"satisfy":[81],"shell":[82],"but":[84],"concentrate":[85],"curvature":[86,114],"at":[87],"fewer":[88],"sites":[89],"provide":[91],"less":[92,161],"efficient":[93,221],"enclosure.":[94],"To":[95],"compare":[96],"these":[97],"architectural":[98,126,194],"alternatives":[99],"systematically,":[100],"five":[101,108],"representative":[102],"capsid":[103],"architectures":[104,244],"were":[105],"evaluated":[106,150],"using":[107],"operationally":[109],"defined":[110],"criteria:":[111],"enclosure":[112],"efficiency,":[113],"organization,":[115],"vertex":[116],"coordination,":[117],"polygon-class":[118],"economy,":[119],"scalability.":[121,228],"Under":[122],"equal":[123],"weighting,":[124],"normalized":[125],"utility":[127],"was":[128,149,185],"0.40":[129],"for":[130,133,136,139,144,238,255],"tetrahedral,":[131],"0.50":[132],"octahedral,":[134],"0.85":[135],"all-pentamer,":[137],"0.95":[138],"prolate":[140,190],"pentamer\u2013hexamer,":[141],"1.00":[143],"canonical":[145,169],"pentamer\u2013hexamer":[146,170,198,204,243],"architectures.":[147],"Robustness":[148],"by":[151,166,188],"individually":[152],"omitting":[153],"criteria,":[154],"criterion":[156],"weights,":[157],"varying":[159],"directly":[162],"measurable":[163],"scalability":[164],"scores":[165],"\u00b10.5.":[167],"The":[168,229],"generally":[172],"remained":[173],"highest-ranked,":[174],"although":[175],"it":[176],"tied":[177],"with":[178],"or,":[179],"under":[180],"strongest":[182],"asymmetric":[183],"perturbation,":[184],"modestly":[186],"exceeded":[187,196],"its":[189],"variant;":[191],"no":[192],"other":[193,273],"class":[195],"either":[197],"variant.":[199],"These":[200,261],"results":[201],"support":[202],"framework":[205],"as":[206],"particularly":[208],"favorable":[209],"solution":[211],"assumptions":[214],"model,":[217],"combining":[218],"distributed":[219],"curvature,":[220],"enclosure,":[222],"economical":[223],"motif":[224],"use,":[225],"architecture-preserving":[227],"analysis":[230],"provides":[231],"testable":[233],"organizational":[236],"explanation":[237],"recurrent":[240],"use":[241],"in":[245],"capsids,":[247],"not":[249],"establishing":[250],"evolutionary":[251],"causation":[252],"or":[253],"accounting":[254],"molecular":[256],"energetics":[257],"assembly":[259],"kinetics.":[260],"principles":[262],"may":[263],"inform":[265],"design":[267],"synthetic":[269],"cages":[271],"nanoscale":[274],"delivery":[275],"systems.":[276]},"counts_by_year":[],"updated_date":"2026-09-23T05:00:35.095934","created_date":"2026-08-28T00:00:00"}
