Covering the \(k\)-skeleton of the 3-dimensional unit cube by five balls (Q464798)
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scientific article; zbMATH DE number 6362504
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Covering the \(k\)-skeleton of the 3-dimensional unit cube by five balls |
scientific article; zbMATH DE number 6362504 |
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Covering the \(k\)-skeleton of the 3-dimensional unit cube by five balls (English)
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30 October 2014
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Let \(C=[0,1]^3\) be the unit cube in Euclidean \(3\)-space, and define \(r_1\), \(r_2\), and \(r_3\) to be the minimal radii such that the union of all edges of \(C\), the union of all faces of \(C\), and \(C\) itself, respectively, can be covered by \(5\) balls of that radius. The author finds the exact value \(r_1=r_2=r_3=0.5849\dots\) and shows that the corresponding arrangement of balls is unique up to isometries.
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unit cube
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\(k\)-skeleton
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ball covering
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optimization problem
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