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!