Small Volume Bodies of Constant Width with Tetrahedral Symmetries

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Arman, Andrii, Bondarenko, Andriy, Prymak, Andriy, Radchenko, Danylo
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214201
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Small Volume Bodies of Constant Width with Tetrahedral Symmetries. Andrii Arman, Andriy Bondarenko, Andriy Prymak and Danylo Radchenko. SIGMA 21 (2025), 109, 8 pages

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...