Message #2348

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Thu, 19 Jul 2012 14:16:57 -0700

Thanks for the clarification, Roice. I’m sure that I’m not alone in not
understanding much in this discussion and this helps me put it in
greater context. Your recent pictures are worth many thousand words and
make it much more fun to follow the conversation.

-Melinda

On 7/19/2012 8:21 AM, Roice Nelson wrote:
>
>
> 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 <mailto: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
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