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Why do dice have six sides?

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Bog-standard 6-sided dice - Morguefile

They've been with us forever, providing civilization after civilization with convenient,
pocket-sized random-number generators to supply their gaming, gambling, and
entertainment needs.

But of all the shapes in the world, why did they all settle on the cube as the perfect shape for
dice?

Actually, there aren't all that many suitable shapes, considering the needs of game players.
Most importantly, a die has to be fair -- that is, it must have an equal chance
of landing on any of its faces. It also needs to roll well, but not too well,
and have a clearly identifiable top face. Trickier than it sounds.

Fortunately, math provides us the perfect place to get started, with the set of shapes known as the Platonic solids. (That's Platonic as in "Plato," the famous Greek
philosopher, not Platonic as in "having close but non-physical relationships
with each other.")

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Platonic solids are those with flat faces that are the same size and shape, and with corners that have the same number of edges meeting at the same angle. There are five such
shapes, and they're unusually even-looking and pleasing to the eye: the
four-sided, pyramid-like tetrahedron, the six-sided cube, the eight-sided
octahedron, the twelve-sided dodecahedron, and the twenty-sided icosahedron. In
addition to their awesome, nerdy names, their unique, multiple symmetries make
them great starting points for making dice.

All except one, that is. The triangular tetrahedron doesn't really roll -- it has to be thrown
instead -- and it doesn't have a top face, making it awkward to read. They show up in some special-purpose games, but they're too inconvenient for general-purpose use. So next up is the second simplest, the cube.

Turns out the cube has lots of advantages over the other Platonic shapes. It's much easier to carve than the others, for one thing, and its square corners can readily be
checked for evenness. Cubes pack with no wasted space, unlike most polyhedrons.
More complex shapes are harder to make, roll further (and off the table, perhaps)
and just aren't needed. Six possible outcomes (or eleven, if you roll two)
turns out to be just enough for most games.

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Some less-typical varieties of dice - Morguefile

The dodecahedron, the icosahedron, and countless other die shapes still have their niches, notably providing for the assorted random-number needs of complex games like Dungeons and Dragons. D&D players will also be familiar with the non-Platonic ten-sided die, a pentagonal trapezohedron, also used in other
role-playing games to generate percentages.

Strange as it may seem, the contents of the dice bag of a modern role-playing gamer wouldn't be out of place to the gamers of thousands of years ago. A 20-sided glass die from the Roman era sold at auction for over $17,000 back in 2003, making it possibly the most expensive die ever made. We have no idea what game the Romans played with it, although we're fairly sure it didn't have anything to do with wizards, rust monsters, or lightning bolts.

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