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PERFECT AND ALMOST PERFECT HOMOGENEOUS POLYTOPES

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Abstract

The paper is devoted to perfect and almost perfect homogeneous polytopes in Euclidean spaces. We have classified perfect and almost perfect polytopes among all regular polytopes and all semiregular polytopes except Archimedean solids and two four-dimensional Gosset polytopes. Also we have constructed some non-regular homogeneous polytopes that are (or are not) perfect and posed some unsolved questions.

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Acknowledgements

The authors are very grateful to both anonymous reviewers, whose comments and suggestions allowed us to improve the presentation of this article.

Funding

The work of the first author was carried out within the framework of the state Contract to the IM SB RAS, project FWNF-2022-0006.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics of the SB RAS, 4 Acad. Koptyug Ave., Novosibirsk, 630090, Russia

    V. N. Berestovskiĭ

  2. Southern Mathematical Institute of VSC RAS, 53 Vatutina St., Vladikavkaz, 362025, Russia

    Yu. G. Nikonorov

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  1. V. N. Berestovskiĭ
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Correspondence to Yu. G. Nikonorov.

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Professor Anatoly Georgievich Kusraev on the occasion of his 70th birthday.

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Berestovskiĭ, V.N., Nikonorov, Y. . PERFECT AND ALMOST PERFECT HOMOGENEOUS POLYTOPES. J Math Sci 271, 762–777 (2023). https://doi.org/10.1007/s10958-023-06765-8

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