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Answer by Oscar Lanzi for Can solutions to Thomson's problem have pentagons?
Technically, there are best known configurations with pentagons and even with hexagons -- if we allow these polygons to loop around multiple faces. Such configurations may be read from the Wikipedia...
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Thomson's problem asks for the minimum-energy configuration for $N$ electrons on a sphere (refs: https://en.wikipedia.org/wiki/Thomson_problem,...
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