I am on a quest to own every fair die that is mathematically possible. These shapes are known as face-transitive polyhedra, or isohedra. They have the special property that given any two faces, there is some combination of reflections, rotations and translations (Galilean transformations) that maps one face to the other. Because Newtonian Physics is Galilean-invariant, any such shape must then be perfectly mathetmatically fair. What's more, boffins (link?) have painfully classified every single one of them, and there are precisely 30 (if you only count each infinite family once). As a D&D player and a Maths freak, I've always wanted to have a physical copy of all of them, but I haven't gotten serious about it until now. Gotta catch 'em all!