Message #1978

From: Roice Nelson <>
Subject: Re: hemi-puzzles!
Date: Sat, 24 Dec 2011 00:47:39 -0600

Here’s a little more on the {3,5} 8-Color. These puzzles with asymmetrical
colorings are strange, but they arise naturally from the math that
identifies cells with each other, so I wanted to understand things a little

To do that, I made a graph of the 4 vertices, 10 edges, and 8 faces all
"rolled up". By that I mean each of these features is only shown once,
rather than shown multiple times (with hand waving that "this face is
identified with that one", as the MagicTile presentation requires). An
image of my graph with default MagicTile colors is
and some observations about it are:

I haven’t tried to make sequences to solve it yet, but will. If anyone
solves this puzzle, I’d love to hear about your experience with it!


On Fri, Dec 23, 2011 at 12:59 PM, Roice Nelson <> wrote:

> Hi all,
> I added some hemi-puzzles, all ones we haven’t seen before. The
> hemi-dodecahedron and hemi-cube are not new, but I made them vertex turning
> this time. There are also hemi-octahedron and hemi-icosahedron puzzles
> now. All of these have the topology of the projective plane.
> I also stumbled upon a {3,5} 8-Color puzzle. The coloring is not
> symmetrical (like the {8,3} 10-Color and some of the other hyperbolic
> puzzles). It turns out to have 8 faces, 10 edges, and 4 vertices, so the Euler
> Characteristic <> shows
> it has the topology of a sphere. I’ll try to write a little more about
> this 8C puzzle soon.
> You can download the latest by clicking here<>
> .
> Happy Holidays,
> Roice