Message #2306

From: Don Hatch <hatch@plunk.org>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Wed, 04 Jul 2012 01:15:52 -0400

Hi Andrey,

Maybe I finally get what you mean now…
there is a unique plane that contains
the three points at infinity where three edges of the tet come closest to meeting;
I didn’t see that before.
But are you sure the tet faces meet that plane
at a right angle as you claimed?
I believe the tet faces meet the sphere-at-infinity at right angles;
I don’t think both can be true.

And I don’t understand what you mean by "a structure of regular infinite
4-graph without loops" at all.
By "4-graph", do you mean every node has degree 4,
and by "without loops", do you mean a tree?
But I don’t see any such tree in what we’re talking about, so I’m lost :-(

Don

On Wed, Jul 04, 2012 at 04:03:38AM -0000, Andrey wrote:
>
>
> And cutting triangles are planar (i.e. H2), not sperical.
> Their position is selected so that triangles have minimal possible size
> (in the narrowest point of the "vertex"). I’ll try to draw one face of the
> object, but it will be not easy.
> Looks like this combination of truncated tetrahedra will be convex in H3
> (and have a structure of regular infinite 4-graph without loops).
>
> Andrey
>
> — In 4D_Cubing@yahoogroups.com, Don Hatch <hatch@…> wrote:
> >
> > On Tue, Jul 03, 2012 at 03:29:38PM -0400, I wrote:
> > > But each face formed by truncation…
> > > it’s a triangle, not a hexagon, right?
> >
> > Sorry, mental lapse on my part!
> > The hexagons you’re talking about
> > are what’s left of the *original* faces when you truncate
> > a tetrahedron.
> > Don’t know where my mind went.
> >
> > Don
> >
>
>

–
Don Hatch
hatch@plunk.org
http://www.plunk.org/~hatch/