Small Volume Bodies of Constant Width with Tetrahedral Symmetries
For every $n\ge 2$, we construct a body $U_n$ of constant width $2$ in $\mathbb{E}^n$ with small volume and symmetries of a regular $n$-simplex. $U_2$ is the Reuleaux triangle. To the best of our knowledge, $U_3$ 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 $U_3$ 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 $n$, the volume of $U_n$ is smaller than the volume of the ball of radius $0.891$.
Authors
- Danylo Radchenko (ORCID: https://orcid.org/0000-0003-1457-6214)
- Andrii Arman (ORCID: https://orcid.org/0000-0003-1462-5733)
- Andriy Prymak (ORCID: https://orcid.org/0000-0002-5022-0154)
- Andriy Bondarenko (ORCID: https://orcid.org/0000-0002-2303-8525)
Institutions
- Norwegian University of Science and Technology (NO)
- Université de Lille (FR)
- Laboratoire Paul Painlevé (FR)
- Laboratoire de Physique des Plasmas (FR)
- University of Manitoba (CA)
Publication Details
- Journal
- Symmetry Integrability and Geometry Methods and Applications
- Published
- 2025-12-21
- DOI
- https://doi.org/10.3842/sigma.2025.109
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Norges Forskningsråd
- Natural Sciences and Engineering Research Council of Canada
- Division of Mathematical Sciences