Message #3218

From: Roice Nelson <>
Subject: Re: [MC4D] Visualizing Hyperbolic Honeycombs
Date: Wed, 11 Nov 2015 18:26:54 -0600

Thanks Melinda! I didn’t know about Shapeways supporting voxel format -
that’s great. It’s been two years since we focused on the physical models,
but we are planning some more and this is really good to know.

Since you like the catacombs, I bet you’ll like this…

  1. Download this hires equirectangular projection:
  2. Go to this link:
  3. Use the folder icon at the bottom right to open the downloaded file.
    You might have to try twice (I did).
  4. Voilà, the catacombs in immersive 3D :D Have a look around with the
    A,S,D,W keys.

Henry, Vi Hart, and I were playing with that one evening, and started to
make an immersive video too, but haven’t finished. A fun goal in this
direction is an immersive experience with hyperbolic transformations of the
catacombs, rather than only traversing them in a euclidean fashion. That
would result in all sorts of bizarre warping of the ceiling and red


On Wed, Nov 11, 2015 at 3:56 PM, Melinda Green
[4D_Cubing] <> wrote:

> 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