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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An algorithmic approach to Rupert’s problem
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by Jakob Steininger and Sergey Yurkevich HTML | PDF
Math. Comp. 92 (2023), 1905-1929 Request permission


A polyhedron $\mathbf {P} \subset \mathbb {R}^3$ has Rupert’s property if a hole can be cut into it, such that a copy of $\mathbf {P}$ 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’s property. A commonly believed conjecture states that every convex polyhedron is Rupert. We prove that Rupert’s 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 not Rupert.
Additional Information
  • Jakob Steininger
  • Affiliation: Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Austria
  • Email:
  • Sergey Yurkevich
  • Affiliation: Department of Mathematics, University of Vienna and Inria, Saclay, Oskar-Morgenstern-Platz 1, Room 02.124, Vienna, 1090, Austria
  • MR Author ID: 1488630
  • Email:
  • Received by editor(s): April 30, 2022
  • Received by editor(s) in revised form: December 24, 2022
  • Published electronically: February 28, 2023
  • Additional Notes: The second author was financially supported by the DOC fellowship of the ÖAW (26101), the WTZ collaboration project of the OeAD (FR 09/2021) and the DeRerumNatura project ANR-19-CE40-0018.
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 1905-1929
  • DOI:
  • MathSciNet review: 4570346