Message #2360

From: Eduard Baumann <>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Thu, 26 Jul 2012 10:39:01 +0200


—– Original Message —–
From: Roice Nelson
Sent: Thursday, July 26, 2012 5:32 AM
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}

On Mon, Jul 23, 2012 at 1:39 PM, Don Hatch wrote:

Yes!  I'd love to see an animation.<br>
Especially an animation in which the boundary of one of the &#123;3,8&#125;s is fixed<br>
and the rest of the picture moves.

If the fixed &#123;3,8&#125; is the &quot;outer&quot;<br>
(or lower-half-plane, or southern hemisphere) one,<br>
then we'll get the usual effect of panning around in hyperbolic 2-space&#58;<br>
(both within the &#123;3,8&#125; itself, and, reflected, in the rest of the picture).

But if we fix a &#42;different&#42; &#123;3,8&#125;...<br>
that's what I'm really wanting to see.<br>
I think that would help me break my mind's insistence<br>
on thinking the &#123;3,8&#125; has 8 &quot;special&quot; closest neighbors,<br>
when it really doesn't.

Here ya go! A short video (just 150 frames). It could be improved for sure, but I hope this first attempt is still useful. Feel free to make suggestions (I don’t like the speedup at the end, for instance). The fixed {3,8} boundary is highlighted in blue.