Message #2347

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Thu, 19 Jul 2012 10:21:40 -0500

Hi Melinda,

Thanks, I’m glad you like them! Yeah, these are the 2D cross-sections of
{3,3,n} H3 honeycombs (at the plane-at-infinity in the half-space model).
I don’t hope to get anywhere honestly, other than to enjoy gaining a
better understanding via this path suggested by Don. Until he brought up
the idea, I had never considered investigating this class of honeycombs
this way.

At this point, I could image puzzles based on these honeycombs and their
duals (of which Andrey’s {6,3,3} is one). Face-Turning {3,3,n} puzzles
(with spherical cuts) seem theoretically possible, though programming them
feels like a *monumental *challenge. A much easier path to new puzzles
would be to take a step back to the 2D world, and perhaps make FT puzzles
based on {3,inf} and {3,ultrainf} tilings. Those would have some hope of
shorter-term realization, and it would be cool if MagicTile could support
them someday.

Cheers,
Roice

On Wed, Jul 18, 2012 at 6:45 PM, Melinda Green <melinda@superliminal.com>wrote:

>
>
> These are gorgeous, Roice!
>
> I still don’t understand what they are but you certainly seem to be
> getting somewhere. And you say these are just cross-sections of some 3D
> objects? Where do you hope to get with this? Perhaps the hyperbolic
> equivalent of the IRP puzzles or the generalization of Andrey’s {6,3,3}
> hyperbolic tile? The infinities are the craziest parts.
>
> -Melinda
>
>
> On 7/18/2012 11:29 AM, Roice Nelson wrote:
>
> Here’s one better filled in (guess the code was up to the challenge), and
> also named correctly. Don’t know why I can’t stop flipping p and r!
>
> http://www.gravitation3d.com/roice/math/337_sphere_at_inf.png
>
> And a couple more, for the {3,3,8} and {3,3,11}.
>
> http://www.gravitation3d.com/roice/math/338_sphere_at_inf.png
> http://www.gravitation3d.com/roice/math/3311_sphere_at_inf.png
>
> If you put all 3 in a directory and cycle through them, you can see the
> "umbrella" opening.
>
> Cheers,
> Roice
>
>
>
>
>
>