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

From: William J Poser (wjposer@ldc.upenn.edu)
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:
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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