Thread: "MT colorings"

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I played arround an created 3 new MT colorings.

{3,6} 7C.xml
L7OH2vLyDpF-jmFh9SXHRxevopBKNhvDh8t8wlLF5GjsA0sbOs4SE6MCRWQmo/Eduard/%7B\
3%2C6%7D%207C.xml>

{6,3} 4C.xml
Ti2viLScAMJu5kwQUj0KxkZNPzyH7plUbh3H8MKV08chLSOQ0TvNrxn5rAxLg/Eduard/%7B\
6%2C3%7D%204C.xml>

{4,4} 56C Skew.xml
3q6GWRI2XPH8vQvg6oO761127dlTgYmOmSH8TM6CULploVYvoefJsdESeGL50/Eduard/%7B\
4%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


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I played arround an created 3 new MT colorings.

RTU2ib4vH7L7OH2vLyDpF-jmFh9SXHRxevopBKNhvDh8t8wlLF5GjsA0sbOs4SE6MCRWQmo/Edu=
ard/%7B3%2C6%7D%207C.xml">{3,6} 7C.xml 

.grp.yahoofs.com/v1/cDPPULkKkVGrGTLuBz8QoBb3a7O3Tn5ZSuGRZrXRTDTi2viLScAMJu5=
kwQUj0KxkZNPzyH7plUbh3H8MKV08chLSOQ0TvNrxn5rAxLg/Eduard/%7B6%2C3%7D%204C.xm=
l">{6,3} 4C.xml 

PUJSM5SyrGTLu92cYivrebTGmqmRPQRF4vtRuFl3q6GWRI2XPH8vQvg6oO761127dlTgYmOmSH8=
TM6CULploVYvoefJsdESeGL50/Eduard/%7B4%2C4%7D%2056C%20Skew.xml">{4,4} 56C Sk=
ew.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 Kle=
in group? I started with {6,3} 9C.xml in Klein.

(b) Augm=
enting colors by extending the edgeset with one :2 more.

{4,4} 56C Sk=
ew.xml. I started with {4,4} 49C Skew.xml.

ia">I didn't get from {4,4|7} to {4,4|8}.

<=
FONT face=3D"georgia">In the 'non skew' view there are holes.

=
But is this puzzle still playable?

&nbs=
p;

Kind regards

rgia">Ed

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Cool, thanks Ed :)

About the {4,4} skew puzzles... They will necessarily have a square number
of colors, so the {4,4|8} should have 64 colors. As you found though,
MagicTile will puke if you go above 56. I picked this number because of
the {3,7}, plus it seemed a reasonably high value. I'll add a note to the
instruction page that the maximum number of colors possible is 56 at the
moment.

Even though the program stayed stable when you set it to 56, the puzzles
wouldn't be solvable because of the holes you see. Also, the skew puzzles
are a special thing in that they require extra configuration (Melinda's IRP
files) to go along with them. I'd only experiment with making new
colorings on the flat puzzles.

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 wrote:

>
>
> I played arround an created 3 new MT colorings.
>
> {3,6} 7C.xml
>
>
> {6,3} 4C.xml
>
>
> {4,4} 56C Skew.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
>
>
>

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Cool, thanks Ed :)

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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 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 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 wrote:
>
>>
>>
>> I played arround an created 3 new MT colorings.
>>
>> {3,6} 7C.xml
>>
>>
>> {6,3} 4C.xml
>>
>>
>> {4,4} 56C Skew.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
>>
>>
>>
>
>
>

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Hi Ed,