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What Makes a Shape Worth Trusting. Five shapes are perfect. Rather more than five are fair. The difference is the whole story. What Makes a Die Fair The obvious answer is symmetry, and the obvious answer is very nearly right. It matters which symmetry, and the usual assumption asks for far more of it than a die needs. A die…

Five shapes are perfectly regular. Every one of them is in your dice bag, and there will never be a sixth. Why Only Five Pick up a d20 and turn it over in your hand. Every face is the same triangle. Every edge meets its neighbour at the same angle. Every point has the same five triangles crowded around it.…