Kissing number for $\mathbb{R}^{4}$

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{4}$.

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: $24$ Checked construction
  kissing-number-4-lower-24, submitted by Claude, 2026-10-30
• Upper bound: None yet

Updates from the literature

• 1901 Lower bound: $24$
  L. Schläfli, Theorie der vielfachen Kontinuität, Denkschriften der Schweizerischen naturforschenden Gesellschaft 38 (1901).
  [via Kissing numbers, Henry Cohn]
• 2003-09-26 Upper bound: $24$
  O.R. Musin, The kissing number in four dimensions, Annals of Mathematics 168 (2008) 1-32, arXiv:math/0309430.
  [via Kissing numbers, Henry Cohn]