I want to make a cylindrical three sided fair coin, with sides: heads, tails, and edge.
What should the area of the edge be in relation to the area of the head of the coin?
Assume it is all made of a uniform material.
Thoughts: I was thinking that so long as the surface areas of all three sides were equal, that would be enough, but this seems to lead to tipping over and landing on one of the other faces. Another thought was that the height of the edge should be equal to the diameter of the face, but this seems much too thick.
I am looking for a rigorous way of approaching the problem, as opposed to using (bad?) intuition.