Year: 2026
Type: preprint
Abstract: We prove that the regular truncated octahedron uniquely minimizes surface area among all parallelohedra of fixed volume. Equivalently, every three-dimensional parallelohedron $P$ satisfies \[ \frac{\mathcal H^2(\partial P)}{|P|^{2/3}} \ge \frac{3(1+2\sqrt3)}{4^{2/3}}, \] with equality if and only if $P$ is similar to the regular truncated octahedron. Among the non-truncated Fedorov types we prove a stronger sharp bound, attained uniquely by the regular rhombic dodecahedron.
Source: arXiv (Cornell University)
Authors: Cesaroni, Annalisa, Novaga, Matteo
Institutions: University of Padua, University of Pisa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207716827