I played arround an created 3 new MT colorings. Questions: (a) Diminishing colors= Is {3,6} 7C.xml still in the Torus group? I= Is {6,3} 4C.xml still in the Kle= (b) Augm= {4,4} 56C Sk= ia">I didn't get from {4,4|7} to {4,4|8}. Choosing Expe= Goi= The s=
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I played arround an created 3 new MT colorings.
{3,6} 7C.xml
3%2C6%7D%207C.xml>
{6,3} 4C.xml
6%2C3%7D%204C.xml>
{4,4} 56C Skew.xml
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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by dropping one edgeset:
started with {3,6} 8C.xml in Torus.
in group? I started with {6,3} 9C.xml in Klein.
enting colors by extending the edgeset with one :2 more.
ew.xml. I started with {4,4} 49C Skew.xml.
ctedNumColors 64 created an error.
ng down to 56 did partially work.
kew view shows still the
<=
FONT face=3D"georgia">In the 'non skew' view there are holes.
=
But is this puzzle still playable?
&nbs=
p;
Kind regards
rgia">Ed
I played arround an created 3 new MT colorings. =A0 Questions: (a) Diminishing colors by dropping one edgese= Is {3,6} 7C.xml still in the Torus group? I started with {3,6} 8C.= Is {6,3} 4C.xml still in the Klein group? I started wit= =A0 (b) Augmenting colors by extending the edgeset with one :2 mor= {4,4} 56C Skew.xml. I started with {4,4} 49C Skew.xml. Choosing Exp= Go= The = In the 'non skew'= But is this puzz= =A0 Kind regards "georgia">Ed I played arround an created 3 new MT colorings. =A0 Questions: (a) Diminishing colors by dropping one edgese= Is {3,6} 7C.xml still in the Torus group? I started with {3,6} 8C.= Is {6,3} 4C.xml still in the Klein group? I started wit= =A0 (b) Augmenting colors by extending the edgeset with one :2 mor= {4,4} 56C Skew.xml. I started with {4,4} 49C Skew.xml. Choosing Exp= Go= The = In the 'non skew'= But is this puzz= =A0 Kind regards "georgia">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
>
>
> 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 :)
ey will necessarily have a square number of colors, so the {4,4|8} should h=
ave 64 colors. =A0As you found though, MagicTile will puke if you go above =
56. =A0I picked this number because of the {3,7}, plus it seemed a reasonab=
ly high value. =A0I'll add a note to the instruction page that the maxi=
mum number of colors possible is 56 at the moment.
o 56, the puzzles wouldn't be solvable because of the holes you see. =
=A0Also, the skew puzzles are a special thing in that they require extra co=
nfiguration (Melinda's IRP files) to go along with them. =A0I'd onl=
y experiment with making new colorings on the flat puzzles.
can help figure out the topologies. =A0And if they work, I'll add them=
in!
seeya,
On Mon, Dec 17, 2012 at 9:15 AM, Eduard <ilto:ed.baumann@bluewin.ch" target=3D"_blank">ed.baumann@bluewin.ch>=
wrote:8ex;border-left:1px #ccc solid;padding-left:1ex">
=20=20=20=20=20=20=20=20
t:
xml in Torus.
h {6,3} 9C.xml in Klein.
e.
p>I didn't get from {4,4|7} to {4,4|8}.p>
ectedNumColors 64 created an error.
ing down to 56 did partially work.
skew view shows still the
{4,4|7} torus.pan>
view there are holes.
le still playable?
=20=20=20=20
=20=20=20=20
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From: Roice Nelson <roice3@gmail.com>
Date: Tue, 18 Dec 2012 11:47:45 -0600
Subject: Re: [MC4D] MT colorings
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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
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
>
> 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
>
>>
>>
>> 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,
ght. =A0They are strange and I do not understand them yet! =A0
edges, and 6 vertices, for a Euler Charicteristic of 4. =A0According to wik=
ipedia examples, the topology of this is two disjoint spheres. =A0So I'=
m baffled at the moment about what abstract shape is being represented. =A0=
bstract shape "rolled up", like we've done in the past. =A0=
=A0The green face has 6 vertices and 6 edges, so it looks like a traditiona=
l hexagon in the abstract. =A0But the others are unusual. =A0The white/blue=
/yellow faces have 1 edge and 2 vertices, so they seem more like a line seg=
ment in the abstract (vs. say, a nagon">henagon=A0like we've seen before). =A0I can't make sense=
of it.
, since some identified faces are so close together. =A0Any time identified=
faces are directly adjacent, it's bad news for puzzles. =A0I 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 o=
n that {3,6}.
m> wrote:x #ccc solid;padding-left:1ex">
can help figure out the topologies. =A0And if they work, I'll add them=
in!
seeya,
On Mon, Dec 17, 2012 at 9:15 AM, Eduard <ilto:ed.baumann@bluewin.ch" target=3D"_blank">ed.baumann@bluewin.ch>=
wrote:8ex;border-left:1px #ccc solid;padding-left:1ex">
=20=20=20=20=20=20=20=20
t:
xml in Torus.
h {6,3} 9C.xml in Klein.
e.
p>I didn't get from {4,4|7} to {4,4|8}.p>
ectedNumColors 64 created an error.
ing down to 56 did partially work.
skew view shows still the
{4,4|7} torus.pan>
view there are holes.
le still playable?
=20=20=20=20
=20=20=20=20
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