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.
- 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
- 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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