[extropy-chat] alt dot fair dice

[Hara Ra]

Well, the solid angle approach is interesting, but I wonder about the 
vertices and polygon edges. If you draw a line from an edge to the center, 
are the angles of the two adjoining faces to this line the same?

One way to avoid this is to think of a jumping jack. Make a shape which is 
just the set of lines to the vertices. Here we meed Bucky Fuller - I 
suspect the solutions to the geodesic domes is an equal spherical angle 
approach, so spiky geodesic domes may do the job.

 From a physics point of view, resting on a face represents a lowest 
possible potential energy solution. This leads to two conditions: All faces 
are the same distance from the center and all faces use the same amount of 
solid angle. Also, the figure must be convex, so it completely rests on any 
face.

So, a drastic simplification can be done. Skip the faces. Use a marked 
sphere. Color it any way you want, with any color having an equal total 
area to all other colors. Colored regions do NOT have to be contiguious. 
(like the state of Hawaii).

Unequal areas could make a single sphere for games like craps.

A sphere full of water could use a tiny bubble to indicate which area is on 
top. If there is a dispute, roll it again.

Multidice of different colors could be use. Three cubes, red, green, blue 
and base 6 notation in the order R,G,B provide 6^3 equally probable results.

Nice problem, stupid mickeymouse solutions (sigh)

> > Spike writes:
> > > Can other shapes be made such that there is
> > > equal probability of any face downward?

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=   Hara Ra (aka Gregory Yob)    =
=     harara at sbcglobal.net       =
=   Alcor North Cryomanagement   =
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