From: Dominikus Scherkl (lyratelle@gmx.de)
Date: Tue Jan 12 2010 - 15:40:52 CST
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Am 10.01.2010 21:43, schrieb Marcin 'Qrczak' Kowalczyk:
> 2010/1/10 verdy_p <verdy_p@wanadoo.fr>:
>
>> Hmmm.. due to the spacial distribution of weight, the center of gravity will be WITHIN the half-sphere,
>
> Not necessarily if the pyramid is long enough, and/or the half sphere
> is actually less than half. Then resting on the top of the half sphere
> would be an unstable equilibrium.
>
> Instead of half sphere we can also have 7 faces with wider angles,
> such that the dice laying on one of them has the center of gravity
> above a point lying outside the face. Then the only stable resting
> positions are on the remaining 7 faces.
The usual way to design odd-sided dice is to take twice as many sides
and number them double (so two sides bearing the "1" and so on).
And than you can build a long stick with that many edges and rounded
ends. So a slice of the stick would be a simple 14-hedron.
This is easy to design equaly distributed (Laplace).
The other way would be paste two seven-sided pyramids turned a half
face against each other and "smear" the pasted edge into a zig-zag line.
For 10-sided dice this is so common that you can buy such in any fantasy
shop - they are called "gems". Take a look.
Best regards
- --
Dominikus Scherkl
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