Re: Maybe not even optimal results, just approximations.
- From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
- Date: Tue, 22 Nov 2005 18:29:02 +0000 (UTC)
José Rui Faustino de Sousa wrote:
I am trying to find the best way to pack hard spheres in regular pyramids.
I am only interested in the triangular, square, pentagonal, hexagonal, octagonal and decagonal cases.
The triangular, square and hexagonal cases are easy corresponding to the face centred cubic, body centred cubic and hexagonal close packing crystal lattice packing schemes.
The body-centered cubic lattice is not an optimal packing in a large enough box (quadratic pyramid), in view of Hales' proof of Kepler's conjecture. For all sufficiently thick bodies, near FCC and HCP
packings will be best, since the packing density in the interior is
the only thing which matters asymptotically.
Arnold Neumaier
.
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- Maybe not even optimal results, just approximations.
- From: José Rui Faustino de Sousa
- Maybe not even optimal results, just approximations.
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