The Truncated Octahedral Conjecture
arXiv:2609.00997
Abstract
Among three-dimensional parallelohedra of fixed volume, the Archimedean truncated octahedron uniquely minimizes surface area, affirming a conjecture of K. Bezdek from 2006. The final scalar inequality is verified by an exact computer-assisted certificate.
23 pages. This version simplifies the proof by introducing the Bernstein certificate sooner