When I started playing D&D, I thought, naively, that the 7 standard dice used (well, 6—the d10 and d100 are both the same shape1) would be all of the possible ways to make a fair die. When I learnt that this was not so, that there were 30 or so unique fair dice,2 I knew one thing: I needed them all.
These shapes are known as face-transitive polyhedra, or isohedra, and they're fucking cool!!! Some of them are pretty basic, but others will really have you scratching your head saying "I can't believe it's not non-face-transitive!" They have the special property that given any two faces, there is some combination of reflections, rotations and translations (isometries) that maps one face perfectly to the other. Because Physics is invariant under isometries, any such shape must then be perfectly mathetmatically fair, no matter how wonky it may look.
Some of these isohedra are commercially available, but I have only been able to find 20 of the 30 so far, so I expect that I will have to learn 3D printing to complete my list (exciting!). Here are some pictures of the ones I have so far:
[to do: add images]
1 a pentagonal trapezohedron
2 depending on how you count—I have opinions
