Message #3217

From: Melinda Green <>
Subject: Re: [MC4D] Visualizing Hyperbolic Honeycombs
Date: Wed, 11 Nov 2015 13:56:14 -0800

From honeycombs to catacombs. How cool is that? That’s an incredible
piece of work, Roice! I’m really happy that you and Henry did such a
huge piece of work, are publishing the results, and are sharing them
with us. I can’t claim to understand more than a small fraction of it,
but it’s more than pertinent to anyone interested in creating or solving
puzzles based on hyperbolic tilings. The images alone are incredible,
and your 3D printed models are especially helpful and intriguing. I
appreciate your attention to geometric accuracy with your "banana" edges.

Brandon pointed out to me that Shapeways now supports a voxel format, so
you will no longer need to perform the conversion back to polygons if
you don’t want to. I’ve been printing some fractal models of mine this
way with excellent results. Here’s one example: Just note that the
documentation is thin and even wrong in parts but it should get better
and I can help if needed.

Your 3D Schlafli symbol map is amazing. Your image grids give wonderful
surveys of the mathematical landscapes, and your hyperbolic catacombs
image continues to fascinate me. Incredible job, guys!

On 11/10/2015 5:56 PM, Roice Nelson [4D_Cubing] wrote:
> Hello again,
> I wanted to share a new paper that Henry Segerman and I have been
> working on in the background for the last few years, which we just
> submitted it to the Journal of Mathematics and the Arts.
> Why share with this group? Because the paper was born right here with
> the following thread started by Nan!
> It’s an exciting thread in my opinion, and a nice record of an
> unfolding mathematical investigation. In the paper, we give a shout
> out to Nan and Don, and reference that initial thread.
> We were able to extend upper half space boundary images to all {p,q,r}
> honeycombs, even {∞,∞,∞}. Will someone figure out how to make a
> permutation puzzle out of that honeycomb?!? Believe it or not, I
> suspect it is possible.
> I hope some of you will enjoy reading the paper, or looking at the
> many images it contains. The preprint is here:
> Best,
> Roice