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

From: Jeff Senn (senn@maya.com)
Date: Sat Jan 09 2010 - 16:01:01 CST

• Next message: Marcin 'Qrczak' Kowalczyk: "Re: Seven-sided die (was Re: This just in)"

[Ignoring the fact that this has gotten so off-topic from this list to be absurd:]

I don't think you need to vary the density for such a die to be "fair" -- it is clearly
fair for the 5 sides-- and clearly the odds of landing on either end (vs one of the 5)
can be varied (I *believe* in a continuous function) from nearly 0 to nearly 1.0 by
adjusting the "width". So you simply must choose the correct width... math (and
resultant width) left as the cliched exercise for the reader...

-Jas

On Jan 9, 2010, at 4:16 PM, William J Poser wrote:

>
> 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:
> http://mathworld.wolfram.com/RegularPolyhedron.html
>
> 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.
>
> Bill
>
>
>

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