{"id":"https://openalex.org/W7224596061","doi":"https://doi.org/10.5281/zenodo.23750595","title":"Conway Unfoldings of Level 1 Menger Polycubes","display_name":"Conway Unfoldings of Level 1 Menger Polycubes","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224596061","doi":"https://doi.org/10.5281/zenodo.23750595"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23750595","doi":"https://doi.org/10.5281/zenodo.23750595","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23750595","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.23750595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141816404","display_name":"John Seamons","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Seamons, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5141816404"],"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/T12504","display_name":"Mathematics and Applications","score":0.1873999983072281,"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":0.1873999983072281,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.15530000627040863,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.08919999748468399,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/menger-sponge","display_name":"Menger sponge","score":0.8669999837875366},{"id":"https://openalex.org/keywords/polyominoes","display_name":"polyominoes","score":0.5220000147819519},{"id":"https://openalex.org/keywords/surface-development","display_name":"surface development","score":0.4620000123977661},{"id":"https://openalex.org/keywords/genus","display_name":"genus","score":0.367000013589859},{"id":"https://openalex.org/keywords/plane-tilings","display_name":"plane tilings","score":0.5789999961853027},{"id":"https://openalex.org/keywords/periodic-table","display_name":"periodic table","score":0.3959999978542328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.727400004863739},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6284000277519226},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5562999844551086},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.5160999894142151},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.49219998717308044},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48730000853538513},{"id":"https://openalex.org/C44000306","wikidata":"https://www.wikidata.org/wiki/Q244330","display_name":"Hinge","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.44999998807907104},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C132943942","wikidata":"https://www.wikidata.org/wiki/Q2562511","display_name":"Footprint","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3312000036239624},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.3215999901294708},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3125},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.288100004196167},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23750595","doi":"https://doi.org/10.5281/zenodo.23750595","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23750595","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.23750596","doi":"https://doi.org/10.5281/zenodo.23750596","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23750596","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.23750595","doi":"https://doi.org/10.5281/zenodo.23750595","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23750595","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2915937652","https://openalex.org/W4400342161","https://openalex.org/W7135637348","https://openalex.org/W4410061066","https://openalex.org/W7096934670","https://openalex.org/W6888523788","https://openalex.org/W7097334524","https://openalex.org/W2148125855","https://openalex.org/W3045327047","https://openalex.org/W7098654463"],"abstract_inverted_index":{"We":[0,95],"give":[1],"an":[2,112],"explicit":[3],"affirmative":[4],"answer":[5],"to":[6],"Langerman":[7],"and":[8,46,60,101,125],"Winslow\u2019s":[9],"question":[10],"about":[11],"Conway":[12,88],"unfoldings":[13],"of":[14,28,74],"the":[15,48,97,103],"level-1":[16,71],"Menger":[17,93],"sponge.":[18],"Its":[19],"72":[20],"exposed":[21],"unit":[22],"squares":[23],"develop":[24],"into":[25,81],"36":[26],"columns":[27],"height":[29],"two,":[30],"with":[31],"retained":[32],"hinges":[33],"forming":[34],"a":[35,82,87,126],"path":[36],"through":[37],"all":[38],"surface":[39],"faces.":[40],"The":[41,84],"footprint":[42],"has":[43],"perimeter":[44],"114":[45],"tiles":[47],"plane":[49],"by":[50,77],"translations.":[51],"Cuts":[52],"follow":[53],"unit-cube":[54],"edges,":[55],"no":[56],"face":[57],"is":[58,86],"subdivided,":[59],"coincident":[61],"cut":[62],"edges":[63],"are":[64],"allowed.":[65],"A":[66,114],"second":[67],"construction":[68,105],"covers":[69],"every":[70],"(1,1,n)-Menger":[72],"polycube,":[73],"genus":[75],"4n+1,":[76],"joining":[78],"hinged":[79],"dominoes":[80],"chain.":[83],"contribution":[85],"unfolding":[89],"for":[90],"this":[91],"specific":[92],"family.":[94],"explain":[96],"geometric":[98],"search":[99],"restriction":[100],"prove":[102],"family":[104],"from":[106],"finite":[107],"periodic":[108],"tables,":[109],"printed":[110],"in":[111],"appendix.":[113],"small":[115],"companion":[116],"package":[117],"supplies":[118],"exact":[119],"corner":[120],"maps,":[121],"hinge":[122],"lists,":[123],"templates":[124],"standalone":[127],"integer":[128],"verifier.":[129]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-30T00:00:00"}