{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/every-3-dimensional-convex-body-can-be","title":"Every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies","arxiv_id":"2112.10698","date":"2021-12-20","proceeding":null,"authors":["A. Prymak"],"abstract":"We show that every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies. The previous result was $16$ copies established by Papadoperakis in 1999, while a conjecture by Hadwiger is $8$. We modify Papadoperakis's approach and develop a discretization technique that reduces the problem to verification of feasibility of a number of linear programs with rational coefficients, which is done with computer assistance using exact arithmetic.","url_abs":"https://arxiv.org/abs/2112.10698v2","url_pdf":"https://arxiv.org/pdf/2112.10698v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"every-3-dimensional-convex-body-can-be","repo_url":"https://github.com/andriyprm/h3atmost14","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}