spherical code

Input interpretation

spherical code

Alternate names

Fejes Tóth's problem | spherical packing

Definition

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, and the configuration is called a spherical code (or spherical packing). In 1943, Fejes Tóth proved that for n points, there always exist two points whose distance d is d<=sqrt(4 - csc^2[(π n)/(6(n - 2))]), and that the limit is exact for n = 3, 4, 6, and 12. The problem of spherical packing is therefore sometimes known as the Fejes Tóth's problem. The general problem has not been solved.
More information »

Related terms

kissing number | spherical covering | spherical design | Thomson problem

Related Wolfram Language symbol

SpherePoints

Subject classifications

MathWorld

packing problems | unsolved problems

MSC 2010

51E23
POWERED BY THE WOLFRAM LANGUAGE

Related Queries:

Have a question about using Wolfram|Alpha?Contact Pro Premium Expert Support »

Give us your feedback »