Ken wrote:
> 
> 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?
> >
> > --
> > Twyst
> 
> Yea John, what Twyst said.
> 
>   The web page link I posted earlier has a considerable amount
> of information available about all the known uniform polyhedra
> constructs and gives an overly  brief explanation on how to
> determine the vertices from data represented by  the Wythoff symbol.
> 
> He explains it as:
> 
>    All but one of the uniform polyhedra can be described by use of
> Wythoff symbol. The Wythoff symbol contains three rational numbers
> p, q, and  r, all larger than 1. If two of these numbers are equal
> to 2, the third  one is arbitrary, otherwise only the numerators
> 2, 3, 4, and 5 can occur, and 4 and 5 cannot occur together. There
> are only finitely many ways to choose such p, q, and r. There are
> four kinds of Wythoff symbols (plus one exceptional case)
> 
> The dodecahedron has the formula 3|2 5, therefore, the vertex
> configuration  is {2, 5, 2, 5, 2, 5}. After removing trivial
> faces, simply {5, 5, 5}  remains, that is, 3 pentagons.
> 
>    The vertex configuration is the sequence of faces arranged around
> a vertex. Since vertices are congruent, this sequence is the same for
> all vertices. A regular n-sided polygon (an n-gon) is described by n.
> Star polygons are described by n/d, where n is the number of vertices,
> connected d apart. For example, 5/2 is the pentagram. Some polyhedra
> contain retrograde faces. For example, 4/3 is a square, traversed in
> the opposite direction. A regular 2-gon is degenerate and can be left
> out if it occurs in the formulae.
> 
> This all may make perfect sense to the author, and yourself, but
> it  lost on me. If you could adapt the Wythoff symbols data to your
> example and work out one Pov example it would be appreciated.

It makes vague sense to me; fortunately it isn't necessary to know it
in order to find the points of the regular polyhedra.  For that, all
you need to know is how the points lie in relation to each other, and
apply a little Pythagoras.

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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