Kissing number for $\mathbb{R}^{10}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{10}$.
Lower bound:
$510$
Upper bound:
$553$
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$336$
Checked construction
kissing-number-10-lower-336, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
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Lower bound: $500$
Reference unknown
[via M. Ganzhinov, Highly symmetric lines, Linear Algebra and its Applications 722 (2025) 12-37, arXiv:2207.08266.] -
2018
Upper bound: $553$
F.C. Machado and F.M. de Oliveira Filho, Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry, Experimental Mathematics 27 (2018) 362-369.
[via Kissing numbers, Henry Cohn] -
2022-07-17
Lower bound: $510$
M. Ganzhinov, Highly symmetric lines, Linear Algebra and its Applications 722 (2025) 12-37, arXiv:2207.08266.
[via Kissing numbers, Henry Cohn]