D&D dice help solve ancient mathematical puzzle

Since the earliest days of Dungeons & Dragons, no matter how engaging the fantasy roleplaying campaign, every player has experienced moments of downtime where they sat bored and doodling on a character sheet while the Dungeon Master deals with some other player’s demands or arcane rules minutiae. More often than not, this leads to said player creating ambitious structures out of the game’s signature polyhedral dice.

Now those nerds are all grown up and practicing science instead of magic, and their obsession with a millennia-old puzzle has led them back to D&D’s tetrahedral, or four-sided, dice.

It all has to do with correcting the ancient Greek philosopher Aristotle’s false conclusion that identical tetrahedrons fit together perfectly — like cubes — leaving no gaps or unoccupied space. When this was discovered to be wrong, reports The New York Times, scientists got to work, but they were only able to pack the pyramids so they filled 72 percent of the available space. Next, physicists used hundreds of the four-sided dice, stuffed into various containers like fishbowls, to get better results — nearly 78 percent, surpassing the more famous packing density of spheres (74 percent).

Then, a computer simulation carried out at the University of Michigan achieved 85 percent packing, which is believed to be the densest so far.

Why does it matter how densely you can pack your tetrahedrons? Is it just so that a Dungeon Master can organize his Bag of Holding more efficiently? It turns out the ancient mathematical puzzle may have — wait for it — military applications. A byproduct of this experiment was the discovery of a “quasicrystal” structure made up of tetrahedrons, which may lead to advances in communication and stealth technology. The research was funded by the U.S. Air Force and the National Science Foundation.