Message #2406

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] MT {8,3} 10 colors
Date: Thu, 04 Oct 2012 21:38:35 -0700

Definitely interesting. 2 questions come to mind.

Can you construct a puzzle in which all the octagonal edges contain
digons, and
Can you flip some or all edges in order to create non-orientable
versions?

-Melinda

On 10/4/2012 8:15 PM, Roice Nelson wrote:
> Cool stuff! Taking a look, the underlying abstract shape has 10
> faces, 24 edges, and 16 vertices. So its Euler Characteristic is 2,
> and it has the topology of the sphere. This means the graph of it can
> be drawn on the plane:
>
> http://www.gravitation3d.com/magictile/pics/83/83-10_graph.png
>
> Here is the unrolled version for reference:
>
> http://www.gravitation3d.com/magictile/pics/83/83-10_unrolled.png
>
> The first pic nicely shows how by starting your solution with the
> digons (the "order 2" faces), it will be similar to solving a 3^3
> starting with the middle layer.
>
> The "irregular" octagonal faces are interesting. I initially thought
> these faces were hexagons in the abstract, until I realized they
> shared multiple disjoint edges with the same neighbor. I hadn’t seen
> anything like that before.
>
> Cheers,
> Roice
>
>
> On Fri, Sep 28, 2012 at 4:02 AM, Andrey <andreyastrelin@yahoo.com
> <mailto:andreyastrelin@yahoo.com>> wrote:
>
> {8,3} 10 colors puzzle is an another strange beast. It has four
> faces of order 2 (i.e. each of them has only 2 neighbors), two
> faces of order 4 and 4 "irregular" faces. And if you start to
> solve it from order 2 faces (that is good idea because puzzle is
> the most dense there), you find yourself in situation where you
> have two disjoint unsolved "layers" - around order 4 faces - and
> have to sort pieces and exchange parity/orientation between them
> (like when you solve 3^3 starting with the middle layer).
> And there is a chance to meet parity problem: some 2C pieces are
> identical and if odd number of pairs are swapped, you’ll need to
> solve it (by swapping some pair once more). And repeat sorting of
> order 4 layers again :)
> Nice thing :)
>
> Andrey
>
>
>
>