What do you know about the statistical accuracy of "strange" dice, such as the d3, d5, d7, d14, d16, d24, or other atypically shaped dice?
I can cover this. It depends on how the die is constructed. There's a semi-regular polyhedron for 24 (you stack a shallow pyramid on each side of a cube), which should be completely fair. For any even number of sides, you can either do two pyramids base-to-base (if it's a multiple of four), sort of like a d8, or two pyramids with a twist (if it's not a multiple of four), like a d10, and those are fair, too. And for any number of faces at all, you can make a prism shape with pointed or rounded ends so it can only land on a side, and that's fair, too. In all of these cases, every face is just like every other face, so barring an off-center weight inside or something, they'll be fair.

If you're talking about other shapes, though, then there's no such guarantee. As Kevin Cook already said on the topic,
In general they are not fair ... but if you properly proportion the sides ... you can make rolls close to fair
Personally, though, I'm enough of a mathematical purist that I wouldn't trust them.