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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 find
a 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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