Draft:Truncated octahedral conjecture

Submission declined on 7 April 2024 by Greenman (talk).

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Declined by Greenman 2 months ago. Last edited by TakuyaMurata 7 seconds ago. Reviewer: Inform author.

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The truncated octahedral conjecture in geometry is intimately related to the Kelvin problem.

Károly Bezdek conjectured in 2006 that the surface area of any parallelohedron of volume 1 cannot be less than that of the truncated octahedral Voronoi cell of the body-centered cubic lattice of volume 1, in Euclidean three space.^[1]

References

^ Bezdek, Károly (2006). "Sphere packings revisited". European Journal of Combinatorics. 27 (6): 864–883. doi:10.1016/j.ejc.2005.05.001. ISSN 0195-6698.

[1] Bezdek, Károly (2006). "Sphere packings revisited". European Journal of Combinatorics. 27 (6): 864–883. doi:10.1016/j.ejc.2005.05.001. ISSN 0195-6698.

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