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The rhombic dodecahedral conjecture
Abstract
We prove that every three-dimensional parallelohedron P satisfies ℋ2(∂ P)≥ 12√2 r(P)2, where r(P) is the inradius of P, with equality if and only if P is similar to the regular rhombic dodecahedron.
Related
BibTeX
@misc{cesaroni2026rhombic,
title = {{The rhombic dodecahedral conjecture}},
author = {Annalisa Cesaroni and Matteo Novaga},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13975},
eprint = {2610.13975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13975},
}
RIS
TY - UNPB
TI - The rhombic dodecahedral conjecture
AU - Annalisa Cesaroni
AU - Matteo Novaga
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.13975
UR - https://arxiv.org/abs/2610.13975
AB - We prove that every three-dimensional parallelohedron P satisfies ℋ^2(∂ P)≥ 12√2 r(P)^2, where r(P) is the inradius of P, with equality if and only if P is similar to the regular rhombic dodecahedron.
ER -