Message #2349

From: Roice Nelson <>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Sat, 21 Jul 2012 17:58:45 -0500

Interesting thoughts/questions! Here are some pictures of the {3,3,8} with
rotations applied to the sphere-at-infinity. Also, I improved the images
to have true stereographic projection of edge widths, which looks much

It would be cool to see a animation with a smoothly changing viewpoint, but
that would take a long time to generate. I’ve been using 100k tets (400k
triangles) for these, and each takes a minute or so to produce on my
laptop. For an animation, each frame needs to be generated all anew (as
the areas that need filling in change depending on the view).


On Thu, Jul 19, 2012 at 12:39 AM, Don Hatch <> wrote:

> These pictures totally rock.
> And yeah, the fact that the overall structure
> on the infinity-plane of the poincare half-space
> ends up following a {n,3} is a total surprise.
> I have no intuition at all about why that would happen.
> I wonder if there are more surprises
> if you do the stereographic projection
> from different point, that’s not in any of the {3,n}’s?
> I think I can imagine what it would look like
> if you chose a point on the boundary of one of the {3,n}’s
> (I think it would follow the structure of a {n,3} in a
> poincare-half-plane).
> But what if you choose a point that’s not
> even on the boundary of any of them?
> I’m not even sure how to find the coords of such a point…
> however I suspect the complement of the union of the {3,n}’s
> has positive fractal dimension, which would imply
> if you just pick a point at random, there’s a nonzero probability
> that it’s not on or in any of the {3,n}’s.
> Don