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.

Ken Tyler

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