Message #2561

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] MT colorings
Date: Tue, 18 Dec 2012 11:47:45 -0600

Hi Ed,

I took a look at your other two colorings last night. They are strange and
I do not understand them yet!

MagicTile reports your {6,3} 4C coloring as having 4 faces, 6 edges, and 6
vertices, for a Euler Charicteristic of 4. According to wikipedia
examples, the topology of this is two disjoint spheres. So I’m baffled at
the moment about what abstract shape is being represented.

I usually understand things better by considering the abstract shape
"rolled up", like we’ve done in the past. The green face has 6 vertices
and 6 edges, so it looks like a traditional hexagon in the abstract. But
the others are unusual. The white/blue/yellow faces have 1 edge and 2
vertices, so they seem more like a line segment in the abstract (vs. say, a
henagon <http://en.wikipedia.org/wiki/Henagon> like we’ve seen before). I
can’t make sense of it.

Sadly, I think neither colorings will make good puzzles, since some
identified faces are so close together. Any time identified faces are
directly adjacent, it’s bad news for puzzles. I didn’t see any slicings
that would work, though a mixed FE slicing on the {3,6} 7C might be
possible. Vertex twisting puzzles are definitely not possible on that {3,6}.

Best,
Roice

On Mon, Dec 17, 2012 at 10:48 AM, Roice Nelson <roice3@gmail.com> wrote:

>
> I’ll check out your first two this eve and see if I can help figure out
> the topologies. And if they work, I’ll add them in!
>
> seeya,
> Roice
>
>
> On Mon, Dec 17, 2012 at 9:15 AM, Eduard <ed.baumann@bluewin.ch> wrote:
>
>>
>>
>> I played arround an created 3 new MT colorings.
>>
>> {3,6} 7C.xml<http://f1.grp.yahoofs.com/v1/cDPPUFI-tIKrGTLuXfjdgxMwPeaV_gFlRTU2ib4vH7L7OH2vLyDpF-jmFh9SXHRxevopBKNhvDh8t8wlLF5GjsA0sbOs4SE6MCRWQmo/Eduard/%7B3%2C6%7D%207C.xml>
>>
>>
>> {6,3} 4C.xml<http://f1.grp.yahoofs.com/v1/cDPPULkKkVGrGTLuBz8QoBb3a7O3Tn5ZSuGRZrXRTDTi2viLScAMJu5kwQUj0KxkZNPzyH7plUbh3H8MKV08chLSOQ0TvNrxn5rAxLg/Eduard/%7B6%2C3%7D%204C.xml>
>>
>>
>> {4,4} 56C Skew.xml<http://f1.grp.yahoofs.com/v1/cDPPUJSM5SyrGTLu92cYivrebTGmqmRPQRF4vtRuFl3q6GWRI2XPH8vQvg6oO761127dlTgYmOmSH8TM6CULploVYvoefJsdESeGL50/Eduard/%7B4%2C4%7D%2056C%20Skew.xml>
>>
>>
>>
>>
>> Questions:
>>
>> (a) Diminishing colors by dropping one edgeset:
>>
>> Is {3,6} 7C.xml still in the Torus group? I started with {3,6} 8C.xml in
>> Torus.
>>
>> Is {6,3} 4C.xml still in the Klein group? I started with {6,3} 9C.xml in
>> Klein.
>>
>>
>>
>> (b) Augmenting colors by extending the edgeset with one :2 more.
>>
>> {4,4} 56C Skew.xml. I started with {4,4} 49C Skew.xml.
>>
>> I didn’t get from {4,4|7} to {4,4|8}.
>>
>> Choosing ExpectedNumColors 64 created an error.
>>
>> Going down to 56 did partially work.
>>
>> The skew view shows still the
>> {4,4|7} torus.
>>
>> In the ‘non skew’ view there are holes.
>>
>> But is this puzzle still playable?
>>
>>
>>
>> Kind regards
>>
>> Ed
>>
>>
>>
>
>
>