Message #1209

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] MHT633 v0.1 uploaded
Date: Wed, 27 Oct 2010 12:46:58 -0500

Andrey,

I’m trying to understand how the infinite {6,3} cells appear to wrap around
on themselves. You did a really nice job making them look like convex
polyhedra…so much so, that when I first looked at the program, I thought
they were dodecahedra!

Would you mind describing the projection to Euclidean space you’re using?
Beltrami-Klein model, Poincare disk model, something else? If you showed
more of the {6,3} cells, would the projection cause these infinite cells to
visually intersect with themselves? (It appears like it would.) More
generally, I’d like to answer the question of what an entire cell would look
like in your projection and in other models. (I think a cell does not live
on a hyperbolic plane, so I’m betting a cell would not be a portion of a
sphere in the Poincare model). Thanks for any insight or references on this
topic you can provide!

Take Care,
Roice

On Wed, Oct 27, 2010 at 10:57 AM, Roice Nelson <roice3@gmail.com> wrote:

> Wow Andrey, this is amazing!
>
> I didn’t even know a {6,3,3} tessellation was attainable. I glossed
> over such possibilities after reading on Wikipedia that there were only 4
> hyperbolic honeycombs. But going back now, I see that claim is "constrained
> by the existence of the regular polyhedra {p,q},{q,r}". So in this case,
> the "regular polyhedron" {p,q} is an infinite hexagonal tiling! (am I
> understanding right?) I’m looking forward to studying this more.
>
> I’d also be curious to hear of any new found knowledge about how you
> determined allowable coloring sets.
>
> I’ve only had a few minutes to play with it, but here are a couple quick
> comments:
>
> - the sticker size slider isn’t working for me, and I wasn’t having much
> luck trying to edit this setting in the settings file either.
> - both of the (b) puzzles crash the program for me, and I have to delete
> the settings file to get the program to start again after that.
> - I would love it if you could implement the auto-spinning as in MC4D. I
> so want to set the thing in motion and watch it for a while to try to
> understand the space better. I’m facing the frustrating feeling people must
> get when they want more from something I make! Care to open source your
> code? :D
>
> Truly Fantastic Andrey!
>
> Roice
>
>
> On Wed, Oct 27, 2010 at 5:19 AM, Andrey <andreyastrelin@yahoo.com> wrote:
>
>> Guess what is it ;)
>>
>>
>> http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/452190950/view?picmode=large&mode=tn&order=title&start=1&dir=asc
>>
>> Program is here:
>>
>> http://games.groups.yahoo.com/group/4D_Cubing/files/MC7D/mht633.zip
>>
>> It is not complete - Save/Load, animation and macros are not implemented,
>> and not tested at all. But there is Help window (for clicks and navigation)
>> - on Ctrl-F1 key. For colors editing and highlighting by mask use Ctrl-Right
>> click on the sticker.
>>
>> My first impression - solving is impossible even for small puzzles:)
>>
>> Good luck )))
>>
>> Andrey
>>
>>
>>
>> ————————————
>>
>> Yahoo! Groups Links
>>
>>
>>
>>
>