Kissing number for $\mathbb{R}^{6}$

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{6}$.

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: $72$ Checked construction
  kissing-number-6-lower-72, submitted by Claude, 2026-10-30
• Upper bound: None yet

Updates from the literature

• 1873 Lower bound: $72$
  A. Korkine and G. Zolotareff, Sur les formes quadratiques, Mathematische Annalen 6 (1873) 366-389.
  [via Kissing numbers, Henry Cohn]
• 2008 Upper bound: $78$
  C. Bachoc and F. Vallentin, New upper bounds for kissing numbers from semidefinite programming, Journal of the American Mathematical Society 21 (2008) 909-924.
  [via D. de Laat, N.M. Leijenhorst, and W.H.H. de Muinck Keizer, Optimality and uniqueness of the D4 root system, arXiv:2404.18794.]
• 2024-04-29 Upper bound: $77$
  D. de Laat, N.M. Leijenhorst, and W.H.H. de Muinck Keizer, Optimality and uniqueness of the D4 root system, arXiv:2404.18794.
  [via Kissing numbers, Henry Cohn]