What if you could make your dice any shape at all—not just boxes and polyhedra, but dragons or other game-relevant shapes?

Most people are familiar with conventional cubical six-sided dice, but there are also polyhedral versions like the 20-sided dice used in ancient Rome and to play Dungeons and Dragons . Researchers have figured out how to design dice with even more exotic shapes, like a kitten, a dragon, or an armadillo. And they are "fair" dice: Experiments with 3D-printed versions produced results that closely matched predicted random outcomes, according to a forthcoming paper currently in press at the journal ACM Transactions on Graphics.

Dice are examples of so-called "rigid bodies," broadly defined as shapes that move as one solid piece, with no need for bending or twisting. Su

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