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Densest dice packing: Tetrahedral dice pack tighter than any other shape

Date:
May 5, 2010
Source:
American Physical Society
Summary:
Tetrahedral dice, which have four triangular sides, pack more densely than any other shape yet tested, according to new research.
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Tetrahedral dice have four triangular faces. When the dice are randomly poured into a container, they pack themselves more tightly than any other shape studied so far.
Credit: Alexander Jaoshvili, Andria Esakia, Massimo Porrati, and Paul M. Chaikin

Tetrahedral dice, which have four triangular sides, pack more densely than any other shape yet tested, according to research performed by a collaboration of New York University and Virginia Tech physicists.

The revelation is the result of a series of experiments that involved pouring tetrahedral dice into containers, shaking them, and adding more dice until the containers were completely filled. After adding water to measure the open space between the dice, the researchers confirmed that the tetrahedrons fill roughly 76% of the available space in a large container. Similar experiments with spheres typically only fill containers to about 64% of the total volume.

The researchers were able to get an inside view of the packed tetrahedral dice by imaging the containers with an MRI machine. The images are vital in helping them check and refine their die packing models.

The experiment, which is reported in the May 3 issue of Physical Review Letters, confirms recent calculations predicting efficient packing. Such packing problems are related to understanding many other problems including liquids seeping through soils, the flow of granular materials like sand and gravel, dense storage of information in digital memory, and even determining the best shapes for packaging consumer products like medicine tablets and candies.

Daan Frankel of the University of Cambridge discusses the tetrahedral packing experiment and related research in a Viewpoint article appearing in the current edition of APS Physics.


Story Source:

The above post is reprinted from materials provided by American Physical Society. Note: Materials may be edited for content and length.


Journal References:

  1. Alexander Jaoshvili, Andria Esakia, Massimo Porrati, Paul M. Chaikin. Experiments on the Random Packing of Tetrahedral Dice. Physical Review Letters, 2010; 104 (18): 185501 DOI: 10.1103/PhysRevLett.104.185501
  2. Daan Frenkel. The tetrahedral dice are cast %u2026 and pack densely. Physics, 2010; 3: 37 DOI: 10.1103/Physics.3.37

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American Physical Society. "Densest dice packing: Tetrahedral dice pack tighter than any other shape." ScienceDaily. ScienceDaily, 5 May 2010. <www.sciencedaily.com/releases/2010/05/100504215932.htm>.
American Physical Society. (2010, May 5). Densest dice packing: Tetrahedral dice pack tighter than any other shape. ScienceDaily. Retrieved September 3, 2015 from www.sciencedaily.com/releases/2010/05/100504215932.htm
American Physical Society. "Densest dice packing: Tetrahedral dice pack tighter than any other shape." ScienceDaily. www.sciencedaily.com/releases/2010/05/100504215932.htm (accessed September 3, 2015).

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