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Dice packing experiment

By sconway - Posted on 05 May 2010

I think Dave needs to test this experiment at home with his collection...

Densest Dice Packing: Tetrahedral Dice Pack Tighter Than Any Other Shape

Science Daily (May 4, 2010)

That's intriguing! It seems as if the same result could be reached by comparing packings various of types of dice with the same volume -- for example, by comparing the volume of the most efficient packing of 50 regular d6s with the most efficient packing of 50 regular d4s (which all have the same individual volume). 

Actually, it would make sense that the fewer the sides of a die, the more efficient it's packing potential. As the die receives more sides, its shape approaches that of a sphere, which, while having a more efficient individual surface area/volume ratio, collectively wastes a lot of packing space. Conversely, as a die loses sides, its shape approaches that of a plane, which, though lacking a high surface area/volume ratio, is most efficient in group packings. Hooray for coins!

sconway's picture

Well put!

In terms of scale, big piles of objects often behave in ways that  are difficult to model, so perhaps that's why they chose the larger sample.

Interesting how often science finds itself testing conventional wisdom. Often results line up as we would expect, but there are also lots of surprises and you don't really know until you check.




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