{"id":"https://openalex.org/W1975100787","doi":"https://doi.org/10.1016/0012-365x(89)90282-3","title":"Three-dimensional analogs of the planar penrose tilings and quasicrystals","display_name":"Three-dimensional analogs of the planar penrose tilings and quasicrystals","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W1975100787","doi":"https://doi.org/10.1016/0012-365x(89)90282-3","mag":"1975100787"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(89)90282-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0012-365x(89)90282-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/0012365X89902823/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/0012365X89902823/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000878855","display_name":"Ludwig Danzer","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"L. Danzer","raw_affiliation_strings":["Mathematisches Institut der Universit\u00e4t, Postfach 50 05 00, D-46 Dortmund 50, F.R. Germany","Mathematisches Institut der Univ., Dortmund, W. Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut der Universit\u00e4t, Postfach 50 05 00, D-46 Dortmund 50, F.R. Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Mathematisches Institut der Univ., Dortmund, W. Germany#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000878855"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.9613,"has_fulltext":true,"cited_by_count":75,"citation_normalized_percentile":{"value":0.83971209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"76","issue":"1","first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9993000030517578,"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":0.9993000030517578,"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/T13443","display_name":"Mineralogy and Gemology Studies","score":0.9456999897956848,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quasicrystal","display_name":"Quasicrystal","score":0.884077250957489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8432559370994568},{"id":"https://openalex.org/keywords/penrose-tiling","display_name":"Penrose tiling","score":0.7692766189575195},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7008405923843384},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6657472252845764},{"id":"https://openalex.org/keywords/substitution-tiling","display_name":"Substitution tiling","score":0.6312981843948364},{"id":"https://openalex.org/keywords/realisation","display_name":"Realisation","score":0.6125113368034363},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4180172085762024},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22757560014724731},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08868393301963806},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07730889320373535},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07453450560569763}],"concepts":[{"id":"https://openalex.org/C203101518","wikidata":"https://www.wikidata.org/wiki/Q263214","display_name":"Quasicrystal","level":2,"score":0.884077250957489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8432559370994568},{"id":"https://openalex.org/C76513542","wikidata":"https://www.wikidata.org/wiki/Q585688","display_name":"Penrose tiling","level":3,"score":0.7692766189575195},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7008405923843384},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6657472252845764},{"id":"https://openalex.org/C21550011","wikidata":"https://www.wikidata.org/wiki/Q7632143","display_name":"Substitution tiling","level":2,"score":0.6312981843948364},{"id":"https://openalex.org/C2779462738","wikidata":"https://www.wikidata.org/wiki/Q17146409","display_name":"Realisation","level":2,"score":0.6125113368034363},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4180172085762024},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22757560014724731},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08868393301963806},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07730889320373535},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07453450560569763},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(89)90282-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0012-365x(89)90282-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/0012365X89902823/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/0012-365x(89)90282-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0012-365x(89)90282-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/0012365X89902823/pdf","source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975100787.pdf","grobid_xml":"https://content.openalex.org/works/W1975100787.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1536486907","https://openalex.org/W1977183350","https://openalex.org/W1988619801","https://openalex.org/W1993750724","https://openalex.org/W2019907608","https://openalex.org/W2044681164","https://openalex.org/W2077036954","https://openalex.org/W2115103988","https://openalex.org/W4234577270","https://openalex.org/W4251111478"],"related_works":["https://openalex.org/W2942385359","https://openalex.org/W2010045655","https://openalex.org/W4388316460","https://openalex.org/W2397912348","https://openalex.org/W4226505356","https://openalex.org/W2004860994","https://openalex.org/W1977071808","https://openalex.org/W1971137224","https://openalex.org/W2808079597","https://openalex.org/W4385890188"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-02T14:50:37.381335","created_date":"2025-10-10T00:00:00"}