The kissing numbers of tetrahedra (Q1913596)
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scientific article; zbMATH DE number 881213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The kissing numbers of tetrahedra |
scientific article; zbMATH DE number 881213 |
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The kissing numbers of tetrahedra (English)
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22 May 1996
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The author shows that there is a lattice packing of tetrahedra such that each tetrahedron contacts 18 others, and that any other packing lattice permits a smaller contact- or kissing-number. So he solves the lattice kissing number problem for the tetrahedron completely. The kissing number for the tetrahedron is remarkably larger than that of the 3-ball, which is 12 according to the famous Newton-Gregory problem. Another surprising phenomenon: The kissing number in the densest lattice packing of tetrahedron is 14, i.e. considerably smaller than the optimum; in contrast to the sphere-case.
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lattice packing
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kissing number problem
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tetrahedron
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