Preprint
Inserted: 19 sep 2026
Last Updated: 19 sep 2026
Year: 2026
Abstract:
We prove that every three-dimensional parallelohedron $P$ satisfies \[ \mathcal H^2(\partial P)\ge 12\sqrt2\,r(P)^2, \] where $r(P)$ is the inradius of $P$, with equality if and only if $P$ is similar to the regular rhombic dodecahedron.
Download: