A survey on the kissing numbers
Peter Boyvalenkov, Stefan Dodunekov, Oleg R. Musin
TL;DR
This survey reviews historical and recent results on kissing numbers, which are the maximum counts of non-overlapping spheres touching a central sphere in various dimensions, linking to spherical codes and packings.
Contribution
It compiles and discusses both old and recent findings on kissing numbers within the broader context of spherical codes and sphere packings.
Findings
Summary of known kissing numbers in various dimensions
Connections between kissing numbers and spherical codes
Overview of bounds and methods in the field
Abstract
The maximum possible number of non-overlapping unit spheres that can touch a unit sphere in dimensions is called kissing number. The problem for finding kissing numbers is closely connected to the more general problems of finding bounds for spherical codes and sphere packings. We survey old and recent results on the kissing numbers keeping the generality of spherical codes.
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Taxonomy
TopicsMathematical Approximation and Integration · Digital Image Processing Techniques · Computational Geometry and Mesh Generation