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PreprintCC BY 4.0arXiv

Local stability for the truncated octahedral conjecture

  • Lark Song
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Abstract

This note proves that the truncated octahedron of Archimedes is a strict local minimizer of the isoperimetric quotient among parallelohedra in three dimensions. This extends the corresponding result from the five-dimensional lattice-Voronoi subclass to the full ten-dimensional local parameter space. A six-zone parametrization and Schur's lemma reduce the Hessian to two positive definite 2× 2 matrices.

Versions

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Cite

BibTeXRIS
BibTeX
@misc{song2026local,
  title = {{Local stability for the truncated octahedral conjecture}},
  author = {Lark Song},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.03093},
  eprint = {2609.03093},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03093},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Local stability for the truncated octahedral conjecture
AU  - Lark Song
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.03093
UR  - https://arxiv.org/abs/2609.03093
AB  - This note proves that the truncated octahedron of Archimedes is a strict local minimizer of the isoperimetric quotient among parallelohedra in three dimensions. This extends the corresponding result from the five-dimensional lattice-Voronoi subclass to the full ten-dimensional local parameter space. A six-zone parametrization and Schur's lemma reduce the Hessian to two positive definite 2× 2 matrices.
ER  -