Small Volume Bodies of Constant Width with Tetrahedral Symmetries
For every ≥ 2, we construct a body ₙ of constant width 2 in ⁿ with small volume and symmetries of a regular -simplex. ₂ is the Reuleaux triangle. To the best of our knowledge, ₃ was not previously constructed, and its volume is smaller than the volume of other three-dimensional bodies of constant w...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214201 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Small Volume Bodies of Constant Width with Tetrahedral Symmetries. Andrii Arman, Andriy Bondarenko, Andriy Prymak and Danylo Radchenko. SIGMA 21 (2025), 109, 8 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862701165122158592 |
|---|---|
| author | Arman, Andrii Bondarenko, Andriy Prymak, Andriy Radchenko, Danylo |
| author_facet | Arman, Andrii Bondarenko, Andriy Prymak, Andriy Radchenko, Danylo |
| citation_txt | Small Volume Bodies of Constant Width with Tetrahedral Symmetries. Andrii Arman, Andriy Bondarenko, Andriy Prymak and Danylo Radchenko. SIGMA 21 (2025), 109, 8 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For every ≥ 2, we construct a body ₙ of constant width 2 in ⁿ with small volume and symmetries of a regular -simplex. ₂ is the Reuleaux triangle. To the best of our knowledge, ₃ was not previously constructed, and its volume is smaller than the volume of other three-dimensional bodies of constant width with tetrahedral symmetries. While the volume of ₃ is slightly larger than the volume of Meissner's bodies of width 2, it exceeds the latter by less than 0.137%. For all large , the volume of ₙ is smaller than the volume of the ball of radius 0.891.
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| first_indexed | 2026-03-18T14:21:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214201 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T14:21:18Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Arman, Andrii Bondarenko, Andriy Prymak, Andriy Radchenko, Danylo 2026-02-20T08:02:34Z 2025 Small Volume Bodies of Constant Width with Tetrahedral Symmetries. Andrii Arman, Andriy Bondarenko, Andriy Prymak and Danylo Radchenko. SIGMA 21 (2025), 109, 8 pages 1815-0659 2020 Mathematics Subject Classification: 52A20; 52A15; 52A23; 52A40; 28A75; 49Q20 arXiv:2406.18428 https://nasplib.isofts.kiev.ua/handle/123456789/214201 https://doi.org/10.3842/SIGMA.2025.109 For every ≥ 2, we construct a body ₙ of constant width 2 in ⁿ with small volume and symmetries of a regular -simplex. ₂ is the Reuleaux triangle. To the best of our knowledge, ₃ was not previously constructed, and its volume is smaller than the volume of other three-dimensional bodies of constant width with tetrahedral symmetries. While the volume of ₃ is slightly larger than the volume of Meissner's bodies of width 2, it exceeds the latter by less than 0.137%. For all large , the volume of ₙ is smaller than the volume of the ball of radius 0.891. We would like to thank anonymous referees for carefully reading the paper and providing valuable feedback. A. Arman acknowledges support in part by a postdoctoral fellowship of the Pacific Institute for the Mathematical Sciences. A. Bondarenko was supported in part by Grant 334466 of the Research Council of Norway, and A. Prymak was supported by NSERC of Canada Discovery Grant RGPIN-2020-05357. D. Radchenko acknowledges funding by the European Union (ERC, FourIntExP, 101078782). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Small Volume Bodies of Constant Width with Tetrahedral Symmetries Article published earlier |
| spellingShingle | Small Volume Bodies of Constant Width with Tetrahedral Symmetries Arman, Andrii Bondarenko, Andriy Prymak, Andriy Radchenko, Danylo |
| title | Small Volume Bodies of Constant Width with Tetrahedral Symmetries |
| title_full | Small Volume Bodies of Constant Width with Tetrahedral Symmetries |
| title_fullStr | Small Volume Bodies of Constant Width with Tetrahedral Symmetries |
| title_full_unstemmed | Small Volume Bodies of Constant Width with Tetrahedral Symmetries |
| title_short | Small Volume Bodies of Constant Width with Tetrahedral Symmetries |
| title_sort | small volume bodies of constant width with tetrahedral symmetries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214201 |
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