Seven-sided die (was Re: This just in)

From: William J Poser (
Date: Sat Jan 09 2010 - 15:16:24 CST

  • Next message: Jeff Senn: "Re: Seven-sided die (was Re: This just in)"

    A seven-sided die is impossible if it is required to be fully symmetric
    like a six-sided die. There is no seven-sided regular polyhedron.
    The five convex regular polyhedra (aka the Platonic solids) have
    4, 6, 8, 12, and 20 sides respectively. See the MathWorld article:

    The seven-sided dice that a Google search turns up are not fully symmetric.
    They have five square faces orthogonal to a pair of pentagonal faces.

    I don't know whether asymmetry necessarily means that the dice are
    not fair. I can imagine that one could make them fair by varying the
    density of the material as a function of location within the die
    in a suitable manner, but I haven't thought/calculated enough to see
    if that would really work, and I don't know enough about the materials
    and manufacturing processes to know how easily such a thing could be
    implemented even if mathematically possible.


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