Twyst wrote:
> 
> Is there any way to explain this in more generalized terms? I was looking
> for information like this recently... But I don't understand where you are
> getting the numbers you're using. Also, is it possible to explain how to get
> stuff like tetrahedrons, and octahedrons, etc, etc?

They way I did it was by taking a twelve-sided die and noting how the
points were oriented around each other.  There are, of course, an
infinite number of ways to hold the die when doing this, but the easiest
way was to orient it so that eight of the points were are the points of a
cube, and the other points lay in the x-y, y-z, or x-z coordinate planes.
Then remembering that each edge is of the same length, I calculated the
points where they would be if the edges were each one unit in length.
I actually did this while extrapolating the dodecahedron to four dimensions
(which resultant shape contains 600 points, 720 sides, 1200 edges and
120 dodecahedrons).

You can calculate the icosahedron and tetrahedron in a similar manner.
The points for the icosahedron are posted both in this newsgroup and in
my rock include file (http://www.erols.com/vansickl/rock.htm)  One set of
points for the tetrahedron works out to:

#local Point0=< .5,0,sqrt(.5)>;
#local Point1=<-.5,0,sqrt(.5)>;
#local Point2=<0, .5,sqrt(.5)>;
#local Point3=<0,-.5,sqrt(.5)>;

(The interested student is invited to check these results.)

The points for the octahedron are simplicity itself,

#local Point0= x;
#local Point1=-x;
#local Point2= y;
#local Point3=-y;
#local Point4= z;
#local Point5=-z;

as are those for the cube:

#local Point0= x+y+z;
#local Point1=-x+y+z;
#local Point2= x-y+z;
#local Point3=-x-y+z;
#local Point4= x+y-z;
#local Point5=-x+y-z;
#local Point6= x-y-z;
#local Point7=-x-y-z;

Somewhere else in this thread someone has quoted some egghead theorems
from some egghead book, but that's not where I got these figures.

Regards,
John
-- 
"Have the manners not to be hittin' the man until he's your husband, and
entitled to hit back!"

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