# 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/