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The kissing number in dimension 11

How many unit spheres in eleven-dimensional Euclidean space can touch one central unit sphere without overlapping each other?

Progress records 2

Understand the problem ↓

2 records · How we rate progress

Understanding the problem

Read the background

How many unit spheres in eleven-dimensional Euclidean space can touch one central unit sphere without overlapping each other?

Fix the dimension at eleven and ask how many equal spheres can surround one equal sphere. After converting sphere centers into normalized directions, each pair must have inner product at most one half. Every pair matters, not just nearby-looking points in a projection.

An arrangement with N directions establishes K(11) ≥ N. To claim K(11) = N, one also needs an upper bound of N. An attractive plot, a low numerical penalty, or a search that stops improving cannot establish optimality.

Why it matters

A fixed dimension provides a concrete target for geometric constructions and certified bounds.

What counts as progress

A new certified lower or upper bound, or an exact determination. Approximate coordinates require a rigorous feasibility argument.

What to watch for

  • Check all point norms and all pairwise separations under the stated normalization.
  • Require exact coordinates, an exact generator, or certified error margins.
  • Track later corrections, independent checks, larger feasible configurations, and upper bounds separately.

Background review: 2026-10-11. Selected sources:

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