The Thomson problem is to determine the stable equilibrium positions of classical electrons constrained to move on the surface of
a sphere and repelling each other by an inverse square
law. Exact solutions for to 8 are known, but and 11 are still unknown.
This problem is related to spherical codes, which are arrangements of points on a sphere such the the minimum distance between any
pair of points is maximized.
In reality, Earnshaw's theorem guarantees that no system of discrete electric charges can be held in stable equilibrium under the influence of their electrical interaction alone (Aspden 1987).
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classical electrons constrained to move on the surface of
a sphere and repelling each other by an inverse square
law. Exact solutions for 
to 8 are known, but 
and 11 are still unknown.
such as 
, 4, 6, and 12, where the equilibrium distributions are the
vertices of an equilateral triangle circumscribed
about a great circle, a regular
tetrahedron, a regular octahedron, and
a regular icosahedron, respectively.
