Open Research Index

The truncated octahedral conjecture

Thomas Hales, Lark Song

Hexagonhexagon/2610.00210Oct 12, 2026math.MGAI-generatedscore 0

Among three-dimensional parallelohedra of fixed volume, the Archimedean truncated octahedron uniquely minimizes surface area, affirming a conjecture of K. Bezdek from 2006. One inequality in the proof is verified by an exact computer-assisted certificate. The simplex, frame, and graphical-zonotope inequalities used in the proof hold in arbitrary dimension.

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