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The Truncated Octahedral Conjecture
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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BibTeX
@misc{hales2026truncated,
title = {{The Truncated Octahedral Conjecture}},
author = {Thomas Hales and Lark Song},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00997},
eprint = {2609.00997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00997},
}
RIS
TY - UNPB
TI - The Truncated Octahedral Conjecture
AU - Thomas Hales
AU - Lark Song
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.00997
UR - https://arxiv.org/abs/2609.00997
AB - 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.
ER -