On the packing of fourteen congruent Spheres in a cube

Joós, Antal

doi:10.1007/s10711-008-9308-3

Cited by 5 publications

(2 citation statements)

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“…To our knowledge, the optimality of d n is proved for n = 2, 3, 4, 5, 6, 8, 9 [10], n = 10 [11] and n = 14 [6]. Optimality of d n was conjectured for an infinite family of packings where p 3 /2 spheres are arranged in a cubic close-packed (ccp) structure [3].…”

Section: Introductionmentioning

confidence: 99%

On Limits of Dense Packing of Equal Spheres in a Cube

Tatarevic¹

2015

Electron. J. Combin.

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We examine packing of n congruent spheres in a cube when n is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of p 3 /2 spheres. For this family of packings, the previous best-known arrangements were usually derived from a ccp by omission of a certain number of spheres without changing the initial structure. In this paper, we show that better arrangements exist for all n p 3 /2 −2. We introduce an optimization method to reveal improvements of these packings, and present many new improvements for n 4629.

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Section: Introductionmentioning

confidence: 99%

On Limits of Dense Packing of Equal Spheres in a Cube

Tatarevic¹

2015

Electron. J. Combin.

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“…The present paper is motivated by the question for which radii there are jammed configurations of n spheres in the d-dimensional unit cube. Many authors have studied densest packings of 50 -100 spheres in squares, triangles, disks and the cube, for certain numbers of spheres also with computer-aided proofs of optimality, see for example [4,9,13,16,24,25,26,27] and the references therein. Nurmela and Östergaard [25] achieved this by minimizing the (smooth) discrete Riesz s-energy of a configuration x of sphere centers x i (for more details on the notation see definition (1) below)…”

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confidence: 99%

A nonsmooth program for jamming hard spheres

Hinow

2012

Optim Lett

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We study packings of n hard spheres of equal radius in the d-dimensional unit cube. We present a nonsmooth function whose local extrema are the radii of jammed packings (where no subset of spheres can be moved keeping all others fixed) and show that for a fixed number of spheres there are only finitely many radii of such jammed configurations. We propose an algorithm for the maximization of this maximal radius function and present examples for 5 -8 disks in the unit square and 4 -6 spheres in the unit cube. The method allows straightforward generalization to packings of spheres in other compact containers.

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