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arXiv · 2609.00997

The Truncated Octahedral Conjecture

Thomas Hales·Lark Song
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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.

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Thomas Hales, Lark Song. 2026-09-11. The Truncated Octahedral Conjecture. https://arxiv.org/abs/2609.00997

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