> krtisfranks wrote:
> > Why restrict this to polygons (two-dimensional space)? I would see this
> > most as star polytopes, which is to say that the domain of reference is
> > least the set of all shapes given by Schlafli symbols that are
> > and which contain at least one positive non-integer rational number
> > possibly in coprime ("lowest") terms); furthermore, it is possible that
> > various trivial reductions could be allowed (for example, lines and
> > polytopes could be considered to be stars without indentations) - I
> > not disallow these possibilities.
> > If we keep it to two-dimensions and keep them regular, than all we need
> > the number of outer vertices and how they are connected (is it every
> > every three, etc.?); my comments about trivial cases still applies. But
> > also think that that it could be useful to have the terbri for outer
> > inner vertices (as you basically already do, although I am not sure
> > they actually are vertices) because they can now easily be referenced
> > conversion.
> Oh, here is a difference: This word is for the shape formed by tracing
> the outline rather than from outer vertex to outer vertex (in my previous
> definition, there actually are only the outer vertices; the inner ones
Okay. I have tried to formalize the concept as follows:
Define a "polytopal hull" to be the minimal hypervolume that is connected,
has a polygonal/polytopal boundary, and which contains (either within its
interior or its boundary) all of the vertices and edges of the
Euclidean-spatial embedding of a graph.
Then this word is the polytopal hull of a graph given by a Schlafli symbol
as described before.
I think that that works.