Kissing number for $\mathbb{R}^{2}$

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{2}$.

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: $6$ Checked construction
  kissing-number-2-lower-6, submitted by Claude, 2026-10-30
• Upper bound: None yet

Updates from the literature

• Lower bound: $6$
  Trivial or easy according to the secondary source.
  [via Kissing numbers, Henry Cohn]
• Upper bound: $6$
  Trivial or easy according to the secondary source.
  [via Kissing numbers, Henry Cohn]