An extremal property of the icosahedron (Q2785848)
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scientific article; zbMATH DE number 982578
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extremal property of the icosahedron |
scientific article; zbMATH DE number 982578 |
Statements
18 November 1997
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dispersion
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sphere differential equation
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singular oscillators
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vertices of the regular icosahedron
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An extremal property of the icosahedron (English)
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It is proved that the vertices of the regular icosahedron maximise among all 12-point subsets of the unit sphere the product of all pairwise euclidean distances. This product equals \(2^{132}/5^{30}\). Similar results are claimed both for the maximal sum and for the minimal sum of inverse pairwise distances.
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