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Recognition of Affine-Equivalent Polyhedra by Their Natural Developments

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Abstract

The classical Cauchy rigidity theorem for convex polytopes reads that if two convex polytopes have isometric developments then they are congruent. In other words, we can decide whether two convex polyhedra are isometric or not by only using their developments. We study a similar problem of whether it is possible to understand that two convex polyhedra in Euclidean 3-space are affine-equivalent by only using their developments.

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Funding

The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. A. Alexandrov

  2. Department of Physics, Novosibirsk State University, Novosibirsk, Russia

    V. A. Alexandrov

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  1. V. A. Alexandrov
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Correspondence to V. A. Alexandrov.

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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 2, pp. 252–275. https://doi.org/10.33048/smzh.2023.64.202

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Alexandrov, V.A. Recognition of Affine-Equivalent Polyhedra by Their Natural Developments. Sib Math J 64, 269–286 (2023). https://doi.org/10.1134/S0037446623020027

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  • DOI: https://doi.org/10.1134/S0037446623020027

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