Message #2356

From: Don Hatch <hatch@plunk.org>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Tue, 24 Jul 2012 06:17:35 -0400

On Mon, Jul 23, 2012 at 09:40:54PM -0500, Roice Nelson wrote:
>
>
> http://www.gravitation3d.com/roice/math/ultrainf/338/338_tet_colored.png
> Each of the four ends of a cell is assigned a different color. The
> neighbor {3,8}s opposite the outer red {3,8} is only composed of the
> other 3 colors (I wonder how many triangles in each of the neighbor
> {3,8}s are associated with the cells connected to just the outer red
> tiling).
>
>
> The answer to my question in parenthesis is 8. Here’s an image of an
> inverted {3,8} and just the neighbor triangles…
> http://www.gravitation3d.com/roice/math/ultrainf/338/338_neighbor_triangles.png

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/