2026
CLM-LR-DRAFT-KISSING4-1= 24EXACT VALUEThe kissing number in four dimensionsSource: Kissing number in four dimensions ↗
PROVEN
Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryResearch Console →The kissing number problem asks how many equal, non-overlapping spheres can simultaneously touch a central sphere of the same size — a question that gets dramatically harder as dimension increases, and is only exactly solved in a handful of dimensions.
The question, scope, and sources behind this Registry record.
What is the maximum number of non-overlapping unit spheres that can simultaneously touch a central unit sphere in four-dimensional Euclidean space?
The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Schütte and van der Waerden. In this paper we present a solution of a long-standing problem about the kissing number in four dimensions. Namely, the equality k(4)=24 is proved. The proof is based on a modification of Delsarte's method.
Kissing number in four dimensionsCurrent frontiers derived from accepted Claims.
The accepted equality closes this optimization result.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.