Building Dice

Here's how anyone with a dice-making machine can create dice that cover any range of numbers. Consider a standard 8-sider. It's made of two square-based pyramids stuck together.

The faces of the pyramids are equilateral triangles. What would happen if, instead of using square-based pyramids, you used pentagon-based pyramids? OK, well that would give you a shape a bit like a spinning top, which had 10 sides. It wouldn't work as a die, because if you rolled it it wouldn't have an uppermost face - it would be a ridge. You can fix that by offsetting the bottom pyramid by half a triangle's width and using kite shapes instead of triangles.

This is how many 10-sided dice today are made. If you went for hexagon-based pyramids, you'd have to use non-equalateral (but still isosceles) triangles so as not to end up with two planes, but hey, that's not hard to do. Also, they would be triangles: you only need to offset the bottom pyramid (and use kites) when it has an odd number of sides.

Now sure, these aren't platonic solids, but they do exhibit the three qualities you need in dice:

1) Every surface is indistinguishable in shape and size from every other surface (unlike the 7-sided dice you showed in KODT #70).

2) When thrown, one surface will be uppermost.

3) The chance of any surface being the uppermost one is exactly the same for all surfaces.

You can use this technique to create dice with any number of faces, although in practice the more faces you want then the bigger the dice would have to be (or the better your eyesight to read the numbers).

So what would, say, a 30-sided die look like? It would consist of two 15-kite pyramids stuck together. You throw it (or toss it, if it's too thin to throw) and one side will be uppermost.

What would a 7-sided die look like? Easy! It would be two 7-kite pyramids stuck together, which each number appearing twice.

That's how to make N-sided dice. They're less painful when stepped on, but easier to mistake for things you ought to be able to eat.

Richard