Thread: "New Klein Quartic puzzle by Gelatinbrain"

From: "Eduard Baumann" <baumann@mcnet.ch>
Date: Thu, 22 Nov 2012 11:40:31 +0100
Subject: Re: [MC4D] New Klein Quartic puzzle by Gelatinbrain



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Very interesting !
Ed

----- Original Message -----=20
From: schuma=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Thursday, November 22, 2012 8:21 AM
Subject: [MC4D] New Klein Quartic puzzle by Gelatinbrain


=20=20=20=20
Hey guys,

Today Gelatinbrain added a new puzzle, called 9.1.1, in his package of pu=
zzles. Mathematically it's the "3C-corner-only" face-turning {7,3} F0.67:0:=
1 (KQ classic). Just ignore the centers and edges and you have it.=20

But, his visualization is quite different. Rather than fitting seven equi=
lateral triangles around a vertex in the hyperbolic space, he fits seven tr=
iangles in an Euclidean space in a folded fashion, pretty much like the inf=
inite regular polyhedra. But in his visualization, the whole puzzle is fini=
te. There's no periodic repetition or so. Gelatinbrain said: "I mapped all =
vertices to equilateral triangles. So there are inevitably broken edges."

The visualization is like this:

http://twistypuzzles.com/forum/download/file.php?id=3D33767

By dragging the puzzle to re-orient it, you can take some inside triangle=
s out. This is not consider a twist, just a change of viewpoint. I played i=
t for a while and I found piece-finding pretty hard. The difficulty is simi=
lar to that of infinite regular polyhedra.

Discussion on twistypuzzles:=20
http://twistypuzzles.com/forum/viewtopic.php?p=3D292407#p292407
and subsequent posts.

Download gelatinbrain:
http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/install.htm
I recommend the "install offline" option. Make sure the java runtime is a=
vailable.

Overall I think this is a great addition to the family of KQ.

Nan



=20=20
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>


Very interesting !

Ed

 

style=3D"BORDER-LEFT: #000000 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: =
0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
----- Original Message -----

style=3D"FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black">Fro=
m:
=20
schuma=
=20

To: ps.com=20
href=3D"mailto:4D_Cubing@yahoogroups.com">4D_Cubing@yahoogroups.com
<=
/DIV>
Sent: Thursday, November 22, 2012 =
8:21=20
AM

Subject: [MC4D] New Klein Quartic =
puzzle=20
by Gelatinbrain


 =20

Hey guys,

Today Gelatinbrain added a new puzzle, called 9.1.1, =
in=20
his package of puzzles. Mathematically it's the "3C-corner-only" face-tur=
ning=20
{7,3} F0.67:0:1 (KQ classic). Just ignore the centers and edges and you h=
ave=20
it.

But, his visualization is quite different. Rather than fittin=
g=20
seven equilateral triangles around a vertex in the hyperbolic space, he f=
its=20
seven triangles in an Euclidean space in a folded fashion, pretty much li=
ke=20
the infinite regular polyhedra. But in his visualization, the whole puzzl=
e is=20
finite. There's no periodic repetition or so. Gelatinbrain said: "I mappe=
d all=20
vertices to equilateral triangles. So there are inevitably broken=20
edges."

The visualization is like this:

href=3D"http://twistypuzzles.com/forum/download/file.php?id=3D33767">http=
://twistypuzzles.com/forum/download/file.php?id=3D33767

By=20
dragging the puzzle to re-orient it, you can take some inside triangles o=
ut.=20
This is not consider a twist, just a change of viewpoint. I played it for=
a=20
while and I found piece-finding pretty hard. The difficulty is similar to=
that=20
of infinite regular polyhedra.

Discussion on twistypuzzles:
=20
href=3D"http://twistypuzzles.com/forum/viewtopic.php?p=3D292407#p292407">=
http://twistypuzzles.com/forum/viewtopic.php?p=3D292407#p292407
and=
=20
subsequent posts.

Download gelatinbrain:
href=3D"http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/ins=
tall.htm">http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/ins=
tall.htm
I=20
recommend the "install offline" option. Make sure the java runtime is=20
available.

Overall I think this is a great addition to the family =
of=20
KQ.

Nan



------=_NextPart_000_0014_01CDC8A6.2D61C180--




From: Roice Nelson <roice3@gmail.com>
Date: Thu, 22 Nov 2012 13:52:28 -0600
Subject: Re: [MC4D] New Klein Quartic puzzle by Gelatinbrain



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I agree! It's really intriguing how the shape changes after moving the
viewpoint.

Thank you Nan for being such a great cross-pollinator between these two
groups!

Roice


On Thu, Nov 22, 2012 at 4:40 AM, Eduard Baumann wrote:

> **
>
>
> Very interesting !
> Ed
>
>
> ----- Original Message -----
> *From:* schuma
> *To:* 4D_Cubing@yahoogroups.com
> *Sent:* Thursday, November 22, 2012 8:21 AM
> *Subject:* [MC4D] New Klein Quartic puzzle by Gelatinbrain
>
>
>
> Hey guys,
>
> Today Gelatinbrain added a new puzzle, called 9.1.1, in his package of
> puzzles. Mathematically it's the "3C-corner-only" face-turning {7,3}
> F0.67:0:1 (KQ classic). Just ignore the centers and edges and you have it.
>
> But, his visualization is quite different. Rather than fitting seven
> equilateral triangles around a vertex in the hyperbolic space, he fits
> seven triangles in an Euclidean space in a folded fashion, pretty much like
> the infinite regular polyhedra. But in his visualization, the whole puzzle
> is finite. There's no periodic repetition or so. Gelatinbrain said: "I
> mapped all vertices to equilateral triangles. So there are inevitably
> broken edges."
>
> The visualization is like this:
>
> http://twistypuzzles.com/forum/download/file.php?id=33767
>
> By dragging the puzzle to re-orient it, you can take some inside triangles
> out. This is not consider a twist, just a change of viewpoint. I played it
> for a while and I found piece-finding pretty hard. The difficulty is
> similar to that of infinite regular polyhedra.
>
> Discussion on twistypuzzles:
> http://twistypuzzles.com/forum/viewtopic.php?p=292407#p292407
> and subsequent posts.
>
> Download gelatinbrain:
> http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/install.htm
> I recommend the "install offline" option. Make sure the java runtime is
> available.
>
> Overall I think this is a great addition to the family of KQ.
>
> Nan
>
>
>

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I agree! =A0It's really=A0intriguing=A0how the shape changes after movi=
ng the viewpoint.


Thank you Nan for being such a great c=
ross-pollinator between these two groups!

Roice

<=
br>
On Thu, Nov 22, 2012 at 4:40 AM, Eduard Baumann =
<>baumann@mcnet.ch> wrote:
" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">







=20=20=20=20=20=20=20=20

















Very interesting !

Ed

=A0

-RIGHT:0px;MARGIN-LEFT:5px;MARGIN-RIGHT:0px">

----- Original Message -----



Sent: Thursday, November 22, 2012 8=
:21=20
AM

Subject: [MC4D] New Klein Quartic p=
uzzle=20
by Gelatinbrain


=A0=20

Hey guys,

Today Gelatinbrain added a new puzzle, called 9.1.1, =
in=20
his package of puzzles. Mathematically it's the "3C-corner-only&=
quot; face-turning=20
{7,3} F0.67:0:1 (KQ classic). Just ignore the centers and edges and you h=
ave=20
it.

But, his visualization is quite different. Rather than fittin=
g=20
seven equilateral triangles around a vertex in the hyperbolic space, he f=
its=20
seven triangles in an Euclidean space in a folded fashion, pretty much li=
ke=20
the infinite regular polyhedra. But in his visualization, the whole puzzl=
e is=20
finite. There's no periodic repetition or so. Gelatinbrain said: &quo=
t;I mapped all=20
vertices to equilateral triangles. So there are inevitably broken=20
edges."

The visualization is like this:

p://twistypuzzles.com/forum/download/file.php?id=3D33767" target=3D"_blank"=
>http://twistypuzzles.com/forum/download/file.php?id=3D33767


By=
=20
dragging the puzzle to re-orient it, you can take some inside triangles o=
ut.=20
This is not consider a twist, just a change of viewpoint. I played it for=
a=20
while and I found piece-finding pretty hard. The difficulty is similar to=
that=20
of infinite regular polyhedra.

Discussion on twistypuzzles:
href=3D"http://twistypuzzles.com/forum/viewtopic.php?p=3D292407#p292407" t=
arget=3D"_blank">http://twistypuzzles.com/forum/viewtopic.php?p=3D292407#p2=
92407

and=20
subsequent posts.

Download gelatinbrain:
s.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/install.htm" target=3D"_=
blank">http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/instal=
l.htm


I=20
recommend the "install offline" option. Make sure the java runt=
ime is=20
available.

Overall I think this is a great addition to the family =
of=20
KQ.

Nan










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