Kissing number for $\mathbb{R}^{9}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{9}$.
Lower bound:
$306$
Upper bound:
$363$
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.
-
Lower bound:
$272$
Checked construction
kissing-number-9-lower-272, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
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1971
Lower bound: $306$
J. Leech and N.J.A. Sloane, Sphere packings and error-correcting codes, Canadian Journal of Mathematics 23 (1971) 718-745.
[via Kissing numbers, Henry Cohn] -
2018
Upper bound: $363$
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]