Message #2357

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Wed, 25 Jul 2012 00:18:07 -0500

oops, yeah, that was the {3,3,7}. Here are images for slightly better
bearings, for both the {3,3,7} and {3,3,8} (I replaced the previous image
labeled 338).

http://www.gravitation3d.com/roice/math/ultrainf/337/337_neighbor_triangles.png

http://www.gravitation3d.com/roice/math/ultrainf/338/338_neighbor_triangles.png

I left all the neighbor tets a solid red for now. I think a 7-color won’t
work as a periodic coloring of the outer {3,7} (and hence the tets), but I
can picture painting the 56-color {3,7} onto the outer guy. If we don’t
care that the coloring is periodic or if we allow adjacent colors to be the
same, I bet we could still use 7 colors anyway. Also, I guess there are
some periodic colorings of the {3,8} with fewer colors that might be nice,
a checkerboard for instance.

seeya,
Roice

On Tue, Jul 24, 2012 at 5:17 AM, Don Hatch <hatch@plunk.org> wrote:

>
> Yup :-) But I think you mislabeled the picture–
> This one’s a {3,3,7}, not {3,3,8}, right?
>
> I wonder if there’s a nice coloring of this
> such that each cell’s 4 "feet" (triangles) are the same color?
> Maybe with 7 colors? (I’m not sure whether that actually works.)
> (Even simply highlighting the 4 feet of a single tet would be instructive.)
>
> Actually I’m finding it’s a bit difficult to get my bearings in this
> picture…
> I wonder how it would look to show the entire {3,3,7},
> but with the outer {3,7} and its neighbor tris colored
> (by tet, as suggested above, if it works) and the remaining triangles left
> white?
>
> Don
>
> –
> Don Hatch
> hatch@plunk.org
> http://www.plunk.org/~hatch/
>
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