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Local quadratic isoperimetric stability of the truncated octahedron among parallelohedra
We prove that the Archimedean truncated octahedron is a strict local minimizer of the isoperimetric quotient among all parallelohedra in $\mathbb{R}^3$. After volume normalization and minimization over rotations, the deficit controls the squared Hausdorff distance from the Archimedean cell. This ext
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