Message #2282

From: schuma <mananself@gmail.com>
Subject: Re: Regular abstract polytopes based on {5,3,4} and {4,3,5}
Date: Mon, 18 Jun 2012 07:08:43 -0000

Hi,

I just updated the applet again to include four more weird honeycombs: {6,3,3}, {6,3,4}, {6,3,5} and {4,4,3}. Please check them out if you think everything so far are natural.

I intentionally set the viewpoints of {6,3,4} and {6,3,5} to be identical to those of {5,3,4} and {5,3,5}, respectively. You’ll find that they look similar. I remember when Andrey released his MHT633 puzzle, Roice said that the hexagons looked like pentagons. I’m talking about the same similarity here.

There are more hyperbolic tessellations including the duals of the four new honeycombs:
{3,3,6}, {4,3,6}, {5,3,6}, {3,4,4}

and the self-duals:
{4,4,4}, {6,3,6}, {3,6,3}.

But the vertices of these seven honeycombs are infinitely far away, and the edges are some infinitely long straight lines. Since my applet is based on the coordinates of the vertices, including these seven honeycombs requires significant changes. Maybe another visualization such as a Poincare model makes more sense.

Nan

— In 4D_Cubing@yahoogroups.com, "schuma" <mananself@…> wrote:
>
> Hi guys,
> I’ve added the six spherical polytopes (platonic solids), and the
> trivial cubic tessellation in Euclidean space, to the applet
> <http://people.bu.edu/nanma/InsideH3/H3.html> . The polytope/honeycombs
> are arranged in a table.
> The natural next step is to understand the tessellations with infinite
> cells and vertex figures, like {6,3,3}.
> Nan
> > — In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@> wrote:>> Hi>
> > Even though there are existing youtube videos and> programs, S3 would
> still> be a nice addition to your applet. It’s great> to be able to run
> this stuff> right on a web page, without anything to> install.> >
> Cheers,> Roice>>
>