{"id":"https://openalex.org/W7224934823","doi":"https://doi.org/10.5281/zenodo.23796742","title":"Icosahedral Quasicrystals as Fibonacci-Modified Icosagrids Projected from the E8 Lattice \u2014 E8 Intelligence Research","display_name":"Icosahedral Quasicrystals as Fibonacci-Modified Icosagrids Projected from the E8 Lattice \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7224934823","doi":"https://doi.org/10.5281/zenodo.23796742"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23796742","doi":"https://doi.org/10.5281/zenodo.23796742","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23796742","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23796742","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153285007","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153285007"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9746000170707703,"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":0.9746000170707703,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.02410000003874302,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/icosahedral-quasicrystals","display_name":"icosahedral quasicrystals","score":0.9990000128746033},{"id":"https://openalex.org/keywords/fibonacci-chain","display_name":"Fibonacci chain","score":0.5889999866485596},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.9100000262260437},{"id":"https://openalex.org/keywords/e8-lattice","display_name":"E8 lattice","score":0.8320000171661377},{"id":"https://openalex.org/keywords/icosagrid","display_name":"icosagrid","score":0.8659999966621399},{"id":"https://openalex.org/keywords/icosahedral-symmetry","display_name":"icosahedral symmetry","score":0.8650000095367432},{"id":"https://openalex.org/keywords/a5-group","display_name":"A5 group","score":0.8629999756813049},{"id":"https://openalex.org/keywords/binary-icosahedral-group","display_name":"binary icosahedral group","score":0.9240000247955322}],"concepts":[{"id":"https://openalex.org/C113709186","wikidata":"https://www.wikidata.org/wiki/Q5986738","display_name":"Icosahedral symmetry","level":2,"score":0.9790999889373779},{"id":"https://openalex.org/C203101518","wikidata":"https://www.wikidata.org/wiki/Q263214","display_name":"Quasicrystal","level":2,"score":0.879800021648407},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.8112999796867371},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5982999801635742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.444599986076355},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32919999957084656},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23796742","doi":"https://doi.org/10.5281/zenodo.23796742","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23796742","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23796743","doi":"https://doi.org/10.5281/zenodo.23796743","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23796743","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23796742","doi":"https://doi.org/10.5281/zenodo.23796742","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23796742","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7222895105","https://openalex.org/W7221342670","https://openalex.org/W7170152841","https://openalex.org/W7170054593","https://openalex.org/W7169731848","https://openalex.org/W7170057206","https://openalex.org/W7171159131","https://openalex.org/W7219751961","https://openalex.org/W7222874533","https://openalex.org/W7169753068"],"abstract_inverted_index":{"FINDING:":[0],"Icosahedral":[1],"quasicrystals":[2],"arise":[3],"as":[4],"golden":[5],"(Fibonacci-spaced)":[6],"modifications":[7],"of":[8,74,107,158],"the":[9,18,71,75,79,86,96,108,139,159],"10-plane-set":[10],"icosagrid,":[11],"and":[12,78],"this":[13],"construction":[14],"projects":[15],"directly":[16],"from":[17],"E8":[19,46,98,160],"lattice":[20,48],"in":[21,61,135],"8":[22],"dimensions":[23],"|":[24,63,111],"MATH:":[25],"Fibonacci":[26,76],"chain":[27,77],"spacing":[28],"\u2192":[29,125],"\u03c4":[30,65],"=":[31,33,66,102,105],"(1+\u221a5)/2":[32],"1.618...;":[34],"10":[35,131],"plane":[36,132,140],"sets":[37,133],"with":[38,130],"icosahedral":[39,80,82,88,109,136],"symmetry":[40],"(order-60":[41],"rotational":[42],"group":[43,83],"\u2245":[44],"A5);":[45],"root":[47],"(rank":[49],"8,":[50],"240":[51,97],"roots,":[52],"Coxeter":[53],"number":[54],"30,":[55],"determinant":[56],"1,":[57],"densest":[58],"sphere":[59],"packing":[60],"8D)":[62],"CONNECTION:":[64],"1.618":[67],"(golden":[68],"ratio)":[69],"is":[70,85],"inflation":[72],"factor":[73],"quasicrystal;":[81],"A5":[84],"binary":[87],"group's":[89],"image,":[90],"whose":[91],"120":[92],"elements":[93],"map":[94],"to":[95],"roots":[99],"(2:1);":[100],"icosagrid":[101],"10-fold":[103],"multigrid":[104,129],"dual":[106],"projection":[110],"DEPTH:":[112],"9":[113],"---":[114],"**1.":[115],"Key":[116],"mathematical":[117],"insight**":[118],"Two":[119],"independent":[120],"results":[121],"converge:":[122],"-":[123],"**Icosagrid":[124],"quasicrystal":[126],"(arXiv:1511.07786):**":[127],"A":[128],"arranged":[134],"symmetry,":[137],"when":[138],"spacings":[141],"are":[142],"modulated":[143],"by":[144],"a":[145],"**Fibonacci":[146],"chain**,":[147],"produces":[148],"an":[149],"Author:":[150],"Andrew":[151],"Stewart":[152],"Caldin,":[153],"Independent":[154],"Researcher,":[155],"UK.":[156],"Part":[157],"Intelligence":[161],"Research":[162],"series.":[163],"Platform:":[164],"e8intelligence.com":[165]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-31T00:00:00"}
