{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T08:10:14Z","timestamp":1778746214959,"version":"3.51.4"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"342","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001822","name":"\u00d6sterreichischen Akademie der Wissenschaften","doi-asserted-by":"publisher","award":["26101"],"award-info":[{"award-number":["26101"]}],"id":[{"id":"10.13039\/501100001822","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001822","name":"\u00d6sterreichischen Akademie der Wissenschaften","doi-asserted-by":"publisher","award":["ANR-19-CE40-0018"],"award-info":[{"award-number":["ANR-19-CE40-0018"]}],"id":[{"id":"10.13039\/501100001822","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001822","name":"\u00d6sterreichischen Akademie der Wissenschaften","doi-asserted-by":"publisher","award":["FR 09\/2021"],"award-info":[{"award-number":["FR 09\/2021"]}],"id":[{"id":"10.13039\/501100001822","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["26101"],"award-info":[{"award-number":["26101"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-19-CE40-0018"],"award-info":[{"award-number":["ANR-19-CE40-0018"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["FR 09\/2021"],"award-info":[{"award-number":["FR 09\/2021"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005203","name":"OeAD-GmbH","doi-asserted-by":"publisher","award":["26101"],"award-info":[{"award-number":["26101"]}],"id":[{"id":"10.13039\/501100005203","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005203","name":"OeAD-GmbH","doi-asserted-by":"publisher","award":["ANR-19-CE40-0018"],"award-info":[{"award-number":["ANR-19-CE40-0018"]}],"id":[{"id":"10.13039\/501100005203","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005203","name":"OeAD-GmbH","doi-asserted-by":"publisher","award":["FR 09\/2021"],"award-info":[{"award-number":["FR 09\/2021"]}],"id":[{"id":"10.13039\/501100005203","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A polyhedron\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold upper P subset-of double-struck upper R cubed\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"bold\">P<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo>\n                              \u2282\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbf {P} \\subset \\mathbb {R}^3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    has Rupert\u2019s property if a hole can be cut into it, such that a copy of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold upper P\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"bold\">P<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbf {P}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    can pass through this hole. There are several works investigating this property for some specific polyhedra: for example, it is known that all 5 Platonic and 9 out of the 13 Archimedean solids admit Rupert\u2019s property. A commonly believed conjecture states that every convex polyhedron is Rupert. We prove that Rupert\u2019s problem is algorithmically decidable for polyhedra with algebraic coordinates. We also design a probabilistic algorithm which can efficiently prove that a given polyhedron is Rupert. Using this algorithm we not only confirm this property for the known Platonic and Archimedean solids, but also prove it for one of the remaining Archimedean polyhedra and many others. Moreover, we significantly improve on almost all known Nieuwland numbers and finally conjecture, based on statistical evidence, that the Rhombicosidodecahedron is in fact\n                    <italic>not<\/italic>\n                    Rupert.\n                  <\/p>","DOI":"10.1090\/mcom\/3831","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T10:40:53Z","timestamp":1675248053000},"page":"1905-1929","source":"Crossref","is-referenced-by-count":3,"title":["An algorithmic approach to Rupert\u2019s problem"],"prefix":"10.1090","volume":"92","author":[{"given":"Jakob","family":"Steininger","sequence":"first","affiliation":[]},{"given":"Sergey","family":"Yurkevich","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,2,28]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/PL00009337","article-title":"Largest placement of one convex polygon inside another","volume":"19","author":"Agarwal, P. K.","year":"1998","journal-title":"Discrete Comput. Geom.","ISSN":"https:\/\/id.crossref.org\/issn\/0179-5376","issn-type":"print"},{"issue":"6","key":"2","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1080\/00029890.2021.1901461","article-title":"Cubes and boxes have Rupert\u2019s passages in every nontrivial direction","volume":"128","author":"Bezdek, Andr\u00e1s","year":"2021","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"key":"3","unstructured":"[Cha83] B. Chazelle, The polygon containment problem, Adv. Comput. Res. 1 (1983), 1\u201333."},{"issue":"6","key":"4","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1080\/00029890.2018.1449505","article-title":"Rupert property of Archimedean solids","volume":"125","author":"Chai, Ying","year":"2018","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"key":"5","unstructured":"[Fre22] A. Fredriksson, The triakis tetrahedron and the pentagonal icositetrahedron are Rupert,  arXiv:2210.00601, 2022."},{"issue":"1-2","key":"6","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0747-7171(88)80005-1","article-title":"Solving systems of polynomial inequalities in subexponential time","volume":"5","author":"Grigor\u2032ev, D. Yu.","year":"1988","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"issue":"1","key":"7","first-page":"29","article-title":"Rupert properties of polyhedra and the generalised Nieuwland constant","volume":"23","author":"Hoffmann, Bal\u00e1zs","year":"2019","journal-title":"J. Geom. Graph.","ISSN":"https:\/\/id.crossref.org\/issn\/1433-8157","issn-type":"print"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"87","DOI":"10.4169\/math.mag.90.2.87","article-title":"Platonic passages","volume":"90","author":"Jerrard, Richard P.","year":"2017","journal-title":"Math. Mag.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-570X","issn-type":"print"},{"issue":"10","key":"9","doi-asserted-by":"publisher","first-page":"929","DOI":"10.1080\/00029890.2019.1656958","article-title":"The truncated tetrahedron is Rupert","volume":"126","author":"Lavau, G\u00e9rard","year":"2019","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[Sch50] D. Schreck, Prince Rupert\u2019s problem and its extension by Pieter Nieuwland, Scripta Math. 16 (1950), 73\u201380, 261\u2013267.","DOI":"10.1055\/s-0029-1231769"},{"issue":"9","key":"11","first-page":"241","article-title":"Das Problem des Prinzen Ruprecht von der Pfalz","volume":"10","author":"Scriba, Christoph J.","year":"1968","journal-title":"Praxis Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0032-7042","issn-type":"print"},{"key":"12","unstructured":"[Sha78] M. I. Shamos, Computational Geometry, PhD thesis, USA, 1978. AAI7819047."},{"key":"13","doi-asserted-by":"crossref","unstructured":"[SY22] J. Steininger and S. Yurkevich, Extended abstract for: solving Rupert\u2019s problem algorithmically, ACM Commun. Comput. Algebra 56 (2022), no. 2, 32\u201335.","DOI":"10.1145\/3572867.3572870"},{"key":"14","unstructured":"[Ton18] P. Tonpho, Covering of objects related to Rupert property, 2018. Master Thesis, \\url{http:\/\/cuir.car.chula.ac.th\/handle\/123456789\/73138}."},{"key":"15","unstructured":"[TW22] P. Tonpho and W. Wichiramala, Rupert property of some particular n-simplex and n-octahedrons, June 2022. \\url{https:\/\/www.researchgate.net\/publication\/361602528_{R}upert_{p}roperty_{o}f_{s}ome_{p}articular_{n}-simplex_{a}nd_{n}-octahedrons}."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03831-5\/mcom3831_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03831-5\/S0025-5718-2023-03831-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:59:08Z","timestamp":1776833948000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03831-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,28]]},"references-count":15,"journal-issue":{"issue":"342","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["S0025-5718-2023-03831-5"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3831","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2023,2,28]]}}}