On 9/21/12, Warren Smith <warren.wds@gmail.com> wrote:
Well first of all, if the number N>4 of faces is even, you can use a doubled-version of an (N/2)-sided pyramid [glue two of them together at the common (N/2)-gon base face] to get a dice which clearly has exact uniform probabilities because each face is the same under a symmetry as each other.
Second, re Veit's 2-sided coin problem, the easier and probably better solution for it is to make a non-polyhedral smooth-surfaced convex "coin" got by, e.g. rotating about the y axis, the curve got from a circle of radius=1 centered at (9,0) and horizontal line segments at |y|=1 with |x|<9. The resulting object will have exactly two stable positions on a tabletop.
However, when N is odd such as a 5-sided dice, it is less obvious how to proceed. I have solutions in mind, but I'll keep them secret for a while to get you suitably frustrated, plus their validity is debatable anyhow.
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