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Discussion of "jinda"
[parent] [root]
Comment #4: Re: Generalizing and Etymology
Curtis W Franks (Mon Jul 13 16:34:29 2015)

krtisfranks wrote:
> 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

> at
> > least the set of all shapes given by Schlafli symbols that are
> well-formed
> > and which contain at least one positive non-integer rational number
> (quite
> > possibly in coprime ("lowest") terms); furthermore, it is possible that

> > various trivial reductions could be allowed (for example, lines and
> convex
> > polytopes could be considered to be stars without indentations) - I
would
>
> > not disallow these possibilities.
> > If we keep it to two-dimensions and keep them regular, than all we need

> is
> > the number of outer vertices and how they are connected (is it every
> other,
> > every three, etc.?); my comments about trivial cases still applies. But
I
>
> > also think that that it could be useful to have the terbri for outer
and
> > inner vertices (as you basically already do, although I am not sure
that
> > they actually are vertices) because they can now easily be referenced
via
>
> > conversion.
>
> Oh, here is a difference: This word is for the shape formed by tracing
out
> the outline rather than from outer vertex to outer vertex (in my previous

> definition, there actually are only the outer vertices; the inner ones
are
> illusions).

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.

 Comment #5: Re: Generalizing and Etymology Jonathan (Mon Jul 13 22:50:06 2015) It all comes back to that canlu problem doesn't it? We need to first finda way to deal with dimensionality, then we can deal with distinguishing shapes by dimensionality.Perhaps lujvo can be built out of this for star polytopes.
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