Honeycomb construction on designed foundations reveals geometry-dependent developmental pathways

Honeycomb construction on designed foundations reveals geometry-dependent developmental pathways | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Honeycomb construction on designed foundations reveals geometry-dependent developmental pathways Takayuki Narumi, Ryo Ogawa, Koichi Osaki This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9277573/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 14 You are reading this latest preprint version Abstract Honeycomb construction by honeybees is a classical example of collective structure formation, yet how ordered cell patterns emerge under geometric constraints remains insufficiently understood. Here, we investigated the developmental processes of comb construction using 3D-printed designed foundations with systematically varied symmetry and scale. Hexagonal foundations were prepared at sizes smaller than, slightly larger than, and much larger than typical worker cells, together with a non-natural square lattice foundation. On hexagonal foundations comparable in scale to natural cells, construction proceeded through the formation of dome-like structures that subsequently merged into planar combs. In contrast, on extremely large hexagonal foundations, dome-like intermediates were absent; construction was initiated primarily along edges and ridges and developed predominantly in the direction perpendicular to the foundation. On the square foundation tested here, structures initially followed the orthogonal geometry but were not maintained, and were progressively reorganized into mixed configurations compatible with hexagonal-like packing. Across all conditions, two overlapping processes were consistently observed: local wax attachment and subsequent structural modification associated with the progressive formation of boundaries and reorganization. These results indicate that honeycomb structures cannot be explained by simple template following alone, but instead emerge through the interaction of local attachment, structural modification, and geometry-dependent developmental pathways. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Physics 3D printing honeycomb construction geometric constraints structural modification Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 21 Apr, 2026 Reviews received at journal 19 Apr, 2026 Reviews received at journal 16 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviews received at journal 12 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers agreed at journal 08 Apr, 2026 Reviewers invited by journal 08 Apr, 2026 Editor invited by journal 07 Apr, 2026 Editor assigned by journal 01 Apr, 2026 Submission checks completed at journal 01 Apr, 2026 First submitted to journal 31 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9277573","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":623163856,"identity":"fc8e60cf-a3d5-425d-8c73-21bfa655d7cf","order_by":0,"name":"Takayuki Narumi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYBADHn4exgYGhgNwATbcSmG0ZA9jYwNJWhgMzjAwImvBDewZeA9+rmzbJmN85nD7gx9nDic2SCQwfvjBwJeH2xa+ZMmzbbd5zM42Njb23ABrYZbsYWArxqlF/o2BZCNIy3mgX3g+HE7cfyOBQRrol8QGnLbwGP8EaTHuZ2xs/PMBYstvAlrMwLYY8DY2NvNAHMaG35YDPGaWDedu80icOdg4W+ZMunEDz8M2yx4D3H5hb+AxvtlQdtuevyf9wcc3x6xlG9iTD9/4UXEMZ4ihg2YgBiUDg2MJxGqpgzFqiNYyCkbBKBgFwx4AAER+V20tnun2AAAAAElFTkSuQmCC","orcid":"","institution":"The University of Kitakyushu","correspondingAuthor":true,"prefix":"","firstName":"Takayuki","middleName":"","lastName":"Narumi","suffix":""},{"id":623163857,"identity":"ab1cee93-5128-4076-9344-0c5b53b85109","order_by":1,"name":"Ryo Ogawa","email":"","orcid":"","institution":"Yamaguchi University","correspondingAuthor":false,"prefix":"","firstName":"Ryo","middleName":"","lastName":"Ogawa","suffix":""},{"id":623163858,"identity":"55d148a3-ea55-4745-a81c-2d030c175d13","order_by":2,"name":"Koichi Osaki","email":"","orcid":"","institution":"Kwansei Gakuin University","correspondingAuthor":false,"prefix":"","firstName":"Koichi","middleName":"","lastName":"Osaki","suffix":""}],"badges":[],"createdAt":"2026-03-31 09:24:00","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9277573/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9277573/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107481034,"identity":"e4a03982-0ee3-414e-9218-39e558703493","added_by":"auto","created_at":"2026-04-22 02:15:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6074368,"visible":true,"origin":"","legend":"","description":"","filename":"msnarumi2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9277573/v1_covered_9cbf639b-978a-4feb-bc89-3af61316b805.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Honeycomb construction on designed foundations reveals geometry-dependent developmental pathways","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"3D printing, honeycomb construction, geometric constraints, structural modification","lastPublishedDoi":"10.21203/rs.3.rs-9277573/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9277573/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Honeycomb construction by honeybees is a classical example of collective structure formation, yet how ordered cell patterns emerge under geometric constraints remains insufficiently understood. Here, we investigated the developmental processes of comb construction using 3D-printed designed foundations with systematically varied symmetry and scale. Hexagonal foundations were prepared at sizes smaller than, slightly larger than, and much larger than typical worker cells, together with a non-natural square lattice foundation. On hexagonal foundations comparable in scale to natural cells, construction proceeded through the formation of dome-like structures that subsequently merged into planar combs. In contrast, on extremely large hexagonal foundations, dome-like intermediates were absent; construction was initiated primarily along edges and ridges and developed predominantly in the direction perpendicular to the foundation. On the square foundation tested here, structures initially followed the orthogonal geometry but were not maintained, and were progressively reorganized into mixed configurations compatible with hexagonal-like packing. Across all conditions, two overlapping processes were consistently observed: local wax attachment and subsequent structural modification associated with the progressive formation of boundaries and reorganization. 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