# 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

>

>

>

>

>

>