mam@charm.UUCP (Matthew Marcus) (09/28/84)
<You have a 29% chance of reading this line. Role percentile dice>
One way to construct fair dice with any number of sides >2 is
to use curved sides. Take an n-oganal bipyrimid with 2n sides and file
it so the two planes which meet at the base become one smooth curve.
Each edge is a curved arc beginning at one end of the solid and ending
at the other. There are two vertices, no matter how many sides - the
aforementioned ends. Each side is a piece of a cylindrical surface.
When rolled, the die rests on one of those surfaces, and for odd numbers
of sides, an edge is vertical, so to read the die, you have to pick it up,
rather like a tetrahedral die.
A way to construct such a die is as follows: Start with a
cylinder whose axis is along the x-axis. Slice out a wedge using planes
which contain the z-axis, and whose normals make angles $+- pi over n$ with
the y-axis. The wedge that falls out is 1/n'th of the die. Take n such
wedges and glue them together by their flat sides and you have your die.
--------------------------------------
. .. . .. . .x . .. ... . . . <----axis of cylinder
/ \ <---angle is 2*pi/n
/ \ <---wedge cut out
---------------/=====\--------------- <------cylinder
^
|
face of die (curved)
I thought of this while playing Runequest(tm, copyright, all other legalese)
in which you sometimes have to roll 1-3, at random.