Kissing number for $\mathbb{R}^{13}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{13}$.
Lower bound:
$1154$
Upper bound:
$2064$
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:
$906$
Checked construction
kissing-number-13-lower-906, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
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1999
Lower bound: $1154$
V.A. Zinoviev and T. Ericson, New lower bounds for contact numbers in small dimensions, Problems of Information Transmission 35 (1999) 287-294.
[via Kissing numbers, Henry Cohn] -
2022-02-24
Upper bound: $2064$
N. Leijenhorst and D. de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, Mathematical Programming Computation 16 (2024) 503-534, arXiv:2202.12077.
[via Kissing numbers, Henry Cohn]