Two more cheats for a d7

[jack]

1. No-one says rolling dice has to result in a *face*. It's obviously more convenient, but if you roll your dice in a V-shaped valley, you'll end up with them landing on an edge. And you could get a corner by using a conical well. (Though you need to shake it to make sure it doesn't get stuck.) Then any polyhedron with 7n equivalent faces, or edges, or vertices would do the trick. Unfortunately, I don't think it helps, I think you need 7N faces or regular septagons to get 7N edges or vertices, which you can't have.

2. You can have it in six dimensions, though. A 6-dimensional tetrahedron has seven 5-d-tetrahedral faces.

Comments

[alextfish.livejournal.com]

Surely the thing to do is just make a d14 by analogy with a d10, and just have two copies of each digit in [1,7]?

[cartesiandaemon.livejournal.com]

Doh. For some reason, I'd actually assumed d10s were cheats, no, I see they're perfectly fair (they're not platonic solids, but the shape is one of the valid face-symmetric results for a fair die).

However, I'm sure anything where the symmetry involves just one axis of rotation is a cheat, though inconveniently can't formalise that constraint. It works for seven, but it bugs me because it works for a 100 too, but isn't very elegant for that...