{"id":"https://openalex.org/W7223317331","doi":"https://doi.org/10.5281/zenodo.23606828","title":"The Delian Bond: Samson, Delilah and the Octet Between Kepler's Rhombic Dodecahedron and the Cube","display_name":"The Delian Bond: Samson, Delilah and the Octet Between Kepler's Rhombic Dodecahedron and the Cube","publication_year":2026,"publication_date":"2026-10-24","ids":{"openalex":"https://openalex.org/W7223317331","doi":"https://doi.org/10.5281/zenodo.23606828"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23606828","doi":"https://doi.org/10.5281/zenodo.23606828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23606828","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23606828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158495986","display_name":"DICTO","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"DICTO","raw_affiliation_strings":["Independent artist, Osaka, Japan"],"raw_orcid":"https://orcid.org/0009-0001-2620-2036","affiliations":[{"raw_affiliation_string":"Independent artist, Osaka, Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158495986"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":10,"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/T12504","display_name":"Mathematics and Applications","score":0.6830999851226807,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.6830999851226807,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.09809999912977219,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.04399999976158142,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/octet","display_name":"octet","score":0.5910000205039978},{"id":"https://openalex.org/keywords/cube","display_name":"cube","score":0.4560000002384186},{"id":"https://openalex.org/keywords/regular-tetrahedron","display_name":"regular tetrahedron","score":0.8740000128746033},{"id":"https://openalex.org/keywords/regular-octahedron","display_name":"regular octahedron","score":0.984000027179718},{"id":"https://openalex.org/keywords/space-filling-polyhedra","display_name":"space-filling polyhedra","score":0.8510000109672546},{"id":"https://openalex.org/keywords/convex-polyhedra","display_name":"convex polyhedra","score":0.7289999723434448},{"id":"https://openalex.org/keywords/truncated-cube","display_name":"truncated cube","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C94239619","wikidata":"https://www.wikidata.org/wiki/Q178296","display_name":"Dodecahedron","level":2,"score":0.9186000227928162},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.8252999782562256},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.7372999787330627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6262000203132629},{"id":"https://openalex.org/C198819137","wikidata":"https://www.wikidata.org/wiki/Q188884","display_name":"Octahedron","level":3,"score":0.5900999903678894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5723999738693237},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.5691999793052673},{"id":"https://openalex.org/C119001982","wikidata":"https://www.wikidata.org/wiki/Q866099","display_name":"Stereographic projection","level":2,"score":0.5575000047683716},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.538100004196167},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.5073000192642212},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.46549999713897705},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3671000003814697},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27970001101493835},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.2728999853134155},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2669999897480011},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.26429998874664307}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23606828","doi":"https://doi.org/10.5281/zenodo.23606828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23606828","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23606829","doi":"https://doi.org/10.5281/zenodo.23606829","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23606829","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23606828","doi":"https://doi.org/10.5281/zenodo.23606828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23606828","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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":3,"referenced_works":["https://openalex.org/W2000287066","https://openalex.org/W2048475323","https://openalex.org/W2085359951"],"related_works":["https://openalex.org/W7223555021","https://openalex.org/W7223254937","https://openalex.org/W7221812316","https://openalex.org/W7223099137","https://openalex.org/W7223057258","https://openalex.org/W7223277784","https://openalex.org/W7204222137","https://openalex.org/W2461109154","https://openalex.org/W7221576576","https://openalex.org/W7221534326"],"abstract_inverted_index":{"In":[0],"short.":[1],"Regular":[2],"tetrahedra":[3],"and":[4,37,48,83,104,122,138,160,179,214,231,245,295,320,323,336,343,351],"octahedra":[5],"fill":[6,123,199],"space":[7,53,124],"together:":[8],"the":[9,20,46,63,70,75,78,84,87,90,117,195,217,224,228,237,280,285,299,308,316,324,331,337,361],"octet.":[10],"Join":[11],"each":[12,16,39,198,274],"tetrahedron's":[13,79],"centre":[14,18],"to":[15,34,41,65,115,126],"octahedron's":[17,85],"through":[19,62,315],"face":[21,125],"they":[22],"share,":[23],"cut":[24,110,225,283],"every":[25,49,109,185],"such":[26],"double":[27],"cone":[28],"by":[29],"one":[30,68],"flat":[31],"plane":[32],"parallel":[33],"that":[35,279],"face,":[36],"give":[38],"side":[40],"its":[42,143,318],"own":[43],"centre.":[44],"Slide":[45],"cut,":[47,147,167],"position":[50,69,111],"still":[51],"fills":[52],"with":[54,142,163,168,353],"two":[55,71,118,196,218],"convex":[56,121],"solids,":[57],"from":[58,113],"Kepler's":[59],"rhombic":[60,140],"dodecahedra":[61],"octet":[64],"cubes.":[66],"At":[67],"solids":[72,290],"have":[73,220],"exactly":[74],"same":[76,281],"volume:":[77,222],"piece":[80],"has":[81],"doubled":[82],"halved,":[86],"doubling":[88],"of":[89,135,155,201,311],"ancient":[91],"Delian":[92,206,325],"problem":[93],"in":[94,241,256,330,360],"both":[95],"directions":[96],"at":[97,173,189,208,302,357],"once.":[98],"DICTO":[99],"named":[100],"this":[101,250],"pair":[102,310],"Samson":[103],"Delilah.":[105],"Main":[106],"theorem.":[107],"For":[108],"t":[112,129,149,174,180,190,209],"0":[114],"1":[116,192,211],"pieces":[119,219],"are":[120,266,346],"face:":[127],"for":[128,148,284],"\u2264":[130],"1/3":[131,151],"a":[132,139,152,161,233],"regular":[133,153,234],"tetrahedron":[134],"edge":[136,156,186],"3t":[137],"dodecahedron":[141],"eight":[144],"three-fold":[145],"corners":[146,166],"\u2265":[150],"octahedron":[154],"3(1":[157],"\u2212":[158,177,183,193,212],"t)/2":[159],"cube":[162,286],"four":[164],"alternate":[165],"exact":[169,349],"volumes.":[170],"Theorem":[171,203],"2:":[172],"=":[175,181,191,210],"(2\u221a6":[176],"3)/15":[178],"5/3":[182],"(2/3)\u221a2":[184],"is":[187,271,273],"equal;":[188],"\u221b6/3":[194],"kinds":[197],"half":[200,236],"space.":[202],"3":[204],"(the":[205],"bond):":[207],"(2/3)\u00b72\u22121/3,":[213],"only":[215,288],"there,":[216],"equal":[221],"Samson,":[223,339],"cube,":[226],"twice":[227],"octet's":[229,238],"tetrahedron,":[230],"Delilah,":[232,340],"octahedron,":[235],"octahedron.":[239],"Exact":[240],"\u211a(\u221a6),":[242],"\u211a(\u221a2),":[243],"\u211a(\u221b2)":[244],"\u211a(\u221b6).":[246],"With":[247],"paper":[248],"#48":[249],"gives":[251,307],"DICTO's":[252],"six":[253,265],"DICTONIC":[254,258,341,344],"SOLIDS":[255,342],"three":[257,303],"BONDS":[259],"(golden,":[260],"keyed,":[261],"Delian).":[262],"Not":[263],"all":[264],"new":[267,272],"as":[268],"shapes;":[269],"what":[270],"bond.":[275],"A":[276],"remark":[277,306],"shows":[278],"weighted":[282],"meets":[287],"known":[289],"(truncated":[291],"cubic,":[292],"rectified":[293],"cubic":[294],"Kelvin's":[296],"honeycombs),":[297],"so":[298],"count":[300],"stays":[301],"bonds;":[304],"another":[305],"polar":[309],"#48.":[312],"The":[313,334],"family":[314],"octet,":[317],"equal-edged":[319],"half-and-half":[321],"members":[322],"bond":[326],"were":[327],"not":[328],"found":[329],"sources":[332],"checked.":[333],"ideas,":[335],"names":[338],"BONDS,":[345],"DICTO's;":[347],"computation,":[348],"proofs":[350],"drafting":[352],"Claude":[354],"(Anthropic).":[355],"More":[356],"dictospheres.com.":[358],"View":[359],"app:":[362],"https://kaleidohedra.dictospheres.com/?open=dictonic:delian":[363]},"counts_by_year":[{"year":2026,"cited_by_count":10}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-24T00:00:00"}