{"id":"https://openalex.org/W7170050737","doi":"https://doi.org/10.5281/zenodo.21484629","title":"Quasicrystals: 5-Fold Symmetry, Penrose Tiling, and Icosahedral Golden Ratio Links \u2014 E8 Intelligence Research","display_name":"Quasicrystals: 5-Fold Symmetry, Penrose Tiling, and Icosahedral Golden Ratio Links \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-07-22","ids":{"openalex":"https://openalex.org/W7170050737","doi":"https://doi.org/10.5281/zenodo.21484629"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.21484629","doi":"https://doi.org/10.5281/zenodo.21484629","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21484629","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.21484629","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140658052","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/A5140658052"],"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":1.0,"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":1.0,"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":0.00019999999494757503,"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":0.0,"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/quasicrystals","display_name":"quasicrystals","score":1.0},{"id":"https://openalex.org/keywords/fivefold-symmetry","display_name":"fivefold symmetry","score":0.9089999794960022},{"id":"https://openalex.org/keywords/penrose-tiling","display_name":"Penrose tiling","score":0.9959999918937683},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.8920000195503235},{"id":"https://openalex.org/keywords/icosahedral-symmetry","display_name":"icosahedral symmetry","score":0.9900000095367432},{"id":"https://openalex.org/keywords/quasicrystal-diffraction-patterns","display_name":"quasicrystal diffraction patterns","score":0.9139999747276306},{"id":"https://openalex.org/keywords/aperiodic-structures","display_name":"aperiodic structures","score":0.5979999899864197}],"concepts":[{"id":"https://openalex.org/C203101518","wikidata":"https://www.wikidata.org/wiki/Q263214","display_name":"Quasicrystal","level":2,"score":0.9275000095367432},{"id":"https://openalex.org/C113709186","wikidata":"https://www.wikidata.org/wiki/Q5986738","display_name":"Icosahedral symmetry","level":2,"score":0.9254000186920166},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.8537999987602234},{"id":"https://openalex.org/C76513542","wikidata":"https://www.wikidata.org/wiki/Q585688","display_name":"Penrose tiling","level":3,"score":0.7807000279426575},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5981000065803528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5174000263214111},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4422000050544739},{"id":"https://openalex.org/C84229","wikidata":"https://www.wikidata.org/wiki/Q2116709","display_name":"Translational symmetry","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.38179999589920044},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37940001487731934},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3684000074863434},{"id":"https://openalex.org/C5534955","wikidata":"https://www.wikidata.org/wiki/Q7661343","display_name":"Symmetry operation","level":3,"score":0.36730000376701355},{"id":"https://openalex.org/C101586328","wikidata":"https://www.wikidata.org/wiki/Q899539","display_name":"Cross-ratio","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3560999929904938},{"id":"https://openalex.org/C188374626","wikidata":"https://www.wikidata.org/wiki/Q5914418","display_name":"Mirror symmetry","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C203992732","wikidata":"https://www.wikidata.org/wiki/Q1066315","display_name":"Crystallographic point group","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3041999936103821},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.303600013256073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3021000027656555},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.2606000006198883}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.21484629","doi":"https://doi.org/10.5281/zenodo.21484629","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21484629","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.21484630","doi":"https://doi.org/10.5281/zenodo.21484630","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21484630","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.21484629","doi":"https://doi.org/10.5281/zenodo.21484629","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21484629","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":[],"sustainable_development_goals_aurora":[{"score":0.5314965844154358,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"FINDING:":[0],"Quasicrystals":[1],"exhibit":[2],"5-fold":[3,22,91],"symmetry":[4,58,139],"in":[5,30,35,70,76,90,96,129],"ordered":[6],"but":[7,33,110,140],"non-periodic":[8],"structures,":[9],"with":[10,47,63],"direct":[11],"geometric":[12],"links":[13],"to":[14,67,114],"Penrose":[15,38,101],"tiling":[16,39],"and":[17,95],"icosahedral":[18],"configurations.":[19],"MATH:":[20],"-":[21,37,56,73,85,103,125,132],"symmetry:":[23,134],"rotation":[24],"by":[25],"72\u00b0":[26],"(2\u03c0/5)":[27],"is":[28,112],"forbidden":[29],"periodic":[31,137],"crystals":[32],"allowed":[34],"quasicrystals.":[36],"inflation":[40],"ratio:":[41],"\u03c6":[42,88],"=":[43],"(1+\u221a5)/2":[44],"\u2248":[45,51,54,105,116],"1.618,":[46],"associated":[48],"ratios":[49],"1/\u03c6":[50],"0.618,":[52],"1/\u03c6\u00b2":[53],"0.382.":[55],"Icosahedral":[57],"group:":[59],"H\u2083":[60],"(Coxeter":[61],"group)":[62],"120":[64],"elements,":[65],"linked":[66],"golden":[68],"ratio":[69,87],"vertex":[71],"coordinates.":[72],"Schiffler":[74],"points":[75],"twisted":[77],"icosahedron:":[78],"projective":[79],"geometry":[80],"invariants":[81],"involving":[82],"\u03c6.":[83],"CONNECTION:":[84],"Golden":[86],"appears":[89],"quasicrystal":[92],"diffraction":[93],"patterns":[94],"the":[97,152],"inflation/deflation":[98],"rules":[99],"of":[100,151],"tilings.":[102],"0.786":[104,111],"\u221a(\u03c6)/2?":[106],"Not":[107],"directly":[108],"supported;":[109],"close":[113],"\u03c6/2":[115],"0.809,":[117],"so":[118],"no":[119],"exact":[120],"match":[121],"from":[122],"these":[123,130],"findings.":[124],"Base-60:":[126],"not":[127],"mentioned":[128],"sources.":[131],"Crystallographic":[133],"quasicrystals":[135],"break":[136],"translational":[138],"retain":[141],"rotatio":[142],"Author:":[143],"Andrew":[144],"Stewart":[145],"Caldin,":[146],"Independent":[147],"Researcher,":[148],"UK.":[149],"Part":[150],"E8":[153],"Intelligence":[154],"Research":[155],"series.":[156],"Platform:":[157],"e8intelligence.com":[158]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-07-23T00:00:00"}
